Calculus Examples

$5 {(x^{2} + 3)}^{4} (2 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 {(x^{2} + 3)}^{4} x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.2

Multiply $5$ by $2$ .

$10 {(x^{2} + 3)}^{4} x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.3

Use the Binomial Theorem.

$10 ({(x^{2})}^{4} + 4 {(x^{2})}^{3} \cdot 3 + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 1.4.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 (x^{2 \cdot 4} + 4 {(x^{2})}^{3} \cdot 3 + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.1.2

Multiply $2$ by $4$ .

$10 (x^{8} + 4 {(x^{2})}^{3} \cdot 3 + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.2

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 1.4.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 (x^{8} + 4 x^{2 \cdot 3} \cdot 3 + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.2.2

Multiply $2$ by $3$ .

$10 (x^{8} + 4 x^{6} \cdot 3 + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.3

Multiply $3$ by $4$ .

$10 (x^{8} + 12 x^{6} + 6 {(x^{2})}^{2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.4

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.4.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 (x^{8} + 12 x^{6} + 6 x^{2 \cdot 2} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.4.2

Multiply $2$ by $2$ .

$10 (x^{8} + 12 x^{6} + 6 x^{4} \cdot 3^{2} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.5

Raise $3$ to the power of $2$ .

$10 (x^{8} + 12 x^{6} + 6 x^{4} \cdot 9 + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.6

Multiply $9$ by $6$ .

$10 (x^{8} + 12 x^{6} + 54 x^{4} + 4 x^{2} \cdot 3^{3} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.7

Raise $3$ to the power of $3$ .

$10 (x^{8} + 12 x^{6} + 54 x^{4} + 4 x^{2} \cdot 27 + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.8

Multiply $27$ by $4$ .

$10 (x^{8} + 12 x^{6} + 54 x^{4} + 108 x^{2} + 3^{4}) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.4.9

Raise $3$ to the power of $4$ .

$10 (x^{8} + 12 x^{6} + 54 x^{4} + 108 x^{2} + 81) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.5

Apply the distributive property.

$(10 x^{8} + 10 (12 x^{6}) + 10 (54 x^{4}) + 10 (108 x^{2}) + 10 \cdot 81) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $12$ by $10$ .

$(10 x^{8} + 120 x^{6} + 10 (54 x^{4}) + 10 (108 x^{2}) + 10 \cdot 81) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.6.2

Multiply $54$ by $10$ .

$(10 x^{8} + 120 x^{6} + 540 x^{4} + 10 (108 x^{2}) + 10 \cdot 81) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.6.3

Multiply $108$ by $10$ .

$(10 x^{8} + 120 x^{6} + 540 x^{4} + 1080 x^{2} + 10 \cdot 81) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.6.4

Multiply $10$ by $81$ .

$(10 x^{8} + 120 x^{6} + 540 x^{4} + 1080 x^{2} + 810) x {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.7

Apply the distributive property.

$(10 x^{8} x + 120 x^{6} x + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8

Simplify.

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Step 1.8.1

Multiply $x^{8}$ by $x$ by adding the exponents.

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Step 1.8.1.1

Move $x$ .

$(10 (x \cdot x^{8}) + 120 x^{6} x + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.1.2

Multiply $x$ by $x^{8}$ .

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Step 1.8.1.2.1

Raise $x$ to the power of $1$ .

$(10 (x^{1} x^{8}) + 120 x^{6} x + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(10 x^{1 + 8} + 120 x^{6} x + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.1.3

Add $1$ and $8$ .

$(10 x^{9} + 120 x^{6} x + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.2

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 1.8.2.1

Move $x$ .

$(10 x^{9} + 120 (x \cdot x^{6}) + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.2.2

Multiply $x$ by $x^{6}$ .

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Step 1.8.2.2.1

Raise $x$ to the power of $1$ .

$(10 x^{9} + 120 (x^{1} x^{6}) + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(10 x^{9} + 120 x^{1 + 6} + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.2.3

Add $1$ and $6$ .

$(10 x^{9} + 120 x^{7} + 540 x^{4} x + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.3

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 1.8.3.1

Move $x$ .

$(10 x^{9} + 120 x^{7} + 540 (x \cdot x^{4}) + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.3.2

Multiply $x$ by $x^{4}$ .

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Step 1.8.3.2.1

Raise $x$ to the power of $1$ .

$(10 x^{9} + 120 x^{7} + 540 (x^{1} x^{4}) + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(10 x^{9} + 120 x^{7} + 540 x^{1 + 4} + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.3.3

Add $1$ and $4$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{2} x + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.8.4.1

Move $x$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 (x \cdot x^{2}) + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.4.2

Multiply $x$ by $x^{2}$ .

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Step 1.8.4.2.1

Raise $x$ to the power of $1$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 (x^{1} x^{2}) + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{1 + 2} + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.8.4.3

Add $1$ and $2$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) {(x - 2)}^{4} + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.9

Use the Binomial Theorem.

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} + 4 x^{3} \cdot - 2 + 6 x^{2} {(- 2)}^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10

Simplify each term.

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Step 1.10.1

Multiply $- 2$ by $4$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 6 x^{2} {(- 2)}^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10.2

Raise $- 2$ to the power of $2$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 6 x^{2} \cdot 4 + 4 x {(- 2)}^{3} + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10.3

Multiply $4$ by $6$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 24 x^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10.4

Raise $- 2$ to the power of $3$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 24 x^{2} + 4 x \cdot - 8 + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10.5

Multiply $- 8$ by $4$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + {(- 2)}^{4}) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.10.6

Raise $- 2$ to the power of $4$ .

$(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16) + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.11

Expand $(10 x^{9} + 120 x^{7} + 540 x^{5} + 1080 x^{3} + 810 x) (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16)$ by multiplying each term in the first expression by each term in the second expression.

$10 x^{9} x^{4} + 10 x^{9} (- 8 x^{3}) + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12

Simplify each term.

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Step 1.12.1

Multiply $x^{9}$ by $x^{4}$ by adding the exponents.

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Step 1.12.1.1

Move $x^{4}$ .

$10 (x^{4} x^{9}) + 10 x^{9} (- 8 x^{3}) + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{4 + 9} + 10 x^{9} (- 8 x^{3}) + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.1.3

Add $4$ and $9$ .

$10 x^{13} + 10 x^{9} (- 8 x^{3}) + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.2

Rewrite using the commutative property of multiplication.

$10 x^{13} + 10 \cdot - 8 x^{9} x^{3} + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.3

Multiply $x^{9}$ by $x^{3}$ by adding the exponents.

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Step 1.12.3.1

Move $x^{3}$ .

$10 x^{13} + 10 \cdot - 8 (x^{3} x^{9}) + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} + 10 \cdot - 8 x^{3 + 9} + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.3.3

Add $3$ and $9$ .

$10 x^{13} + 10 \cdot - 8 x^{12} + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.4

Multiply $10$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 10 x^{9} (24 x^{2}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.5

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 10 \cdot 24 x^{9} x^{2} + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.6

Multiply $x^{9}$ by $x^{2}$ by adding the exponents.

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Step 1.12.6.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 10 \cdot 24 (x^{2} x^{9}) + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 10 \cdot 24 x^{2 + 9} + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.6.3

Add $2$ and $9$ .

$10 x^{13} - 80 x^{12} + 10 \cdot 24 x^{11} + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.7

Multiply $10$ by $24$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 x^{9} (- 32 x) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.8

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 \cdot - 32 x^{9} x + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.9

Multiply $x^{9}$ by $x$ by adding the exponents.

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Step 1.12.9.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 \cdot - 32 (x \cdot x^{9}) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.9.2

Multiply $x$ by $x^{9}$ .

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Step 1.12.9.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 \cdot - 32 (x^{1} x^{9}) + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.9.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 \cdot - 32 x^{1 + 9} + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.9.3

Add $1$ and $9$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} + 10 \cdot - 32 x^{10} + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.10

Multiply $10$ by $- 32$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 10 x^{9} \cdot 16 + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.11

Multiply $16$ by $10$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{7} x^{4} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.12

Multiply $x^{7}$ by $x^{4}$ by adding the exponents.

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Step 1.12.12.1

Move $x^{4}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 (x^{4} x^{7}) + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.12.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{4 + 7} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.12.3

Add $4$ and $7$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} + 120 x^{7} (- 8 x^{3}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.13

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} + 120 \cdot - 8 x^{7} x^{3} + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.14

Multiply $x^{7}$ by $x^{3}$ by adding the exponents.

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Step 1.12.14.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} + 120 \cdot - 8 (x^{3} x^{7}) + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.14.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} + 120 \cdot - 8 x^{3 + 7} + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.14.3

Add $3$ and $7$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} + 120 \cdot - 8 x^{10} + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.15

Multiply $120$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 120 x^{7} (24 x^{2}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.16

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 120 \cdot 24 x^{7} x^{2} + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.17

Multiply $x^{7}$ by $x^{2}$ by adding the exponents.

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Step 1.12.17.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 120 \cdot 24 (x^{2} x^{7}) + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.17.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 120 \cdot 24 x^{2 + 7} + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.17.3

Add $2$ and $7$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 120 \cdot 24 x^{9} + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.18

Multiply $120$ by $24$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 x^{7} (- 32 x) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.19

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 \cdot - 32 x^{7} x + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.20

Multiply $x^{7}$ by $x$ by adding the exponents.

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Step 1.12.20.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 \cdot - 32 (x \cdot x^{7}) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.20.2

Multiply $x$ by $x^{7}$ .

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Step 1.12.20.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 \cdot - 32 (x^{1} x^{7}) + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.20.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 \cdot - 32 x^{1 + 7} + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.20.3

Add $1$ and $7$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} + 120 \cdot - 32 x^{8} + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.21

Multiply $120$ by $- 32$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 120 x^{7} \cdot 16 + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.22

Multiply $16$ by $120$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{5} x^{4} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.23

Multiply $x^{5}$ by $x^{4}$ by adding the exponents.

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Step 1.12.23.1

Move $x^{4}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 (x^{4} x^{5}) + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.23.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{4 + 5} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.23.3

Add $4$ and $5$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} + 540 x^{5} (- 8 x^{3}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.24

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} + 540 \cdot - 8 x^{5} x^{3} + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.25

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Step 1.12.25.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} + 540 \cdot - 8 (x^{3} x^{5}) + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.25.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} + 540 \cdot - 8 x^{3 + 5} + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.25.3

Add $3$ and $5$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} + 540 \cdot - 8 x^{8} + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.26

Multiply $540$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 540 x^{5} (24 x^{2}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.27

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 540 \cdot 24 x^{5} x^{2} + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.28

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

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Step 1.12.28.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 540 \cdot 24 (x^{2} x^{5}) + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.28.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 540 \cdot 24 x^{2 + 5} + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.28.3

Add $2$ and $5$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 540 \cdot 24 x^{7} + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.29

Multiply $540$ by $24$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 x^{5} (- 32 x) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.30

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 \cdot - 32 x^{5} x + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.31

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 1.12.31.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 \cdot - 32 (x \cdot x^{5}) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.31.2

Multiply $x$ by $x^{5}$ .

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Step 1.12.31.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 \cdot - 32 (x^{1} x^{5}) + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.31.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 \cdot - 32 x^{1 + 5} + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.31.3

Add $1$ and $5$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} + 540 \cdot - 32 x^{6} + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.32

Multiply $540$ by $- 32$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 540 x^{5} \cdot 16 + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.33

Multiply $16$ by $540$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{3} x^{4} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.34

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 1.12.34.1

Move $x^{4}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 (x^{4} x^{3}) + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.34.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{4 + 3} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.34.3

Add $4$ and $3$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} + 1080 x^{3} (- 8 x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.35

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} + 1080 \cdot - 8 x^{3} x^{3} + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.36

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 1.12.36.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} + 1080 \cdot - 8 (x^{3} x^{3}) + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.36.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} + 1080 \cdot - 8 x^{3 + 3} + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.36.3

Add $3$ and $3$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} + 1080 \cdot - 8 x^{6} + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.37

Multiply $1080$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 1080 x^{3} (24 x^{2}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.38

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 1080 \cdot 24 x^{3} x^{2} + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.39

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 1.12.39.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 1080 \cdot 24 (x^{2} x^{3}) + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.39.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 1080 \cdot 24 x^{2 + 3} + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.39.3

Add $2$ and $3$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 1080 \cdot 24 x^{5} + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.40

Multiply $1080$ by $24$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 x^{3} (- 32 x) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.41

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 \cdot - 32 x^{3} x + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.42

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.12.42.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 \cdot - 32 (x \cdot x^{3}) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.42.2

Multiply $x$ by $x^{3}$ .

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Step 1.12.42.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 \cdot - 32 (x^{1} x^{3}) + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.42.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 \cdot - 32 x^{1 + 3} + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.42.3

Add $1$ and $3$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} + 1080 \cdot - 32 x^{4} + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.43

Multiply $1080$ by $- 32$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 1080 x^{3} \cdot 16 + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.44

Multiply $16$ by $1080$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x \cdot x^{4} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.45

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 1.12.45.1

Move $x^{4}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 (x^{4} x) + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.45.2

Multiply $x^{4}$ by $x$ .

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Step 1.12.45.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 (x^{4} x^{1}) + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.45.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{4 + 1} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.45.3

Add $4$ and $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 x (- 8 x^{3}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.46

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 \cdot - 8 x \cdot x^{3} + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.47

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 1.12.47.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 \cdot - 8 (x^{3} x) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.47.2

Multiply $x^{3}$ by $x$ .

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Step 1.12.47.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 \cdot - 8 (x^{3} x^{1}) + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.47.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 \cdot - 8 x^{3 + 1} + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.47.3

Add $3$ and $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} + 810 \cdot - 8 x^{4} + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.48

Multiply $810$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 x (24 x^{2}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.49

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 \cdot 24 x \cdot x^{2} + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.50

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 1.12.50.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 \cdot 24 (x^{2} x) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.50.2

Multiply $x^{2}$ by $x$ .

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Step 1.12.50.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 \cdot 24 (x^{2} x^{1}) + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.50.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 \cdot 24 x^{2 + 1} + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.50.3

Add $2$ and $1$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 810 \cdot 24 x^{3} + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.51

Multiply $810$ by $24$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} + 810 x (- 32 x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.52

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} + 810 \cdot - 32 x \cdot x + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.53

Multiply $x$ by $x$ by adding the exponents.

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Step 1.12.53.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} + 810 \cdot - 32 (x \cdot x) + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.53.2

Multiply $x$ by $x$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} + 810 \cdot - 32 x^{2} + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.54

Multiply $810$ by $- 32$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 810 x \cdot 16 + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.12.55

Multiply $16$ by $810$ .

$10 x^{13} - 80 x^{12} + 240 x^{11} - 320 x^{10} + 160 x^{9} + 120 x^{11} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.13

Add $240 x^{11}$ and $120 x^{11}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 320 x^{10} + 160 x^{9} - 960 x^{10} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.14

Subtract $960 x^{10}$ from $- 320 x^{10}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 160 x^{9} + 2880 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.15

Add $160 x^{9}$ and $2880 x^{9}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3040 x^{9} - 3840 x^{8} + 1920 x^{7} + 540 x^{9} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.16

Add $3040 x^{9}$ and $540 x^{9}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 3840 x^{8} + 1920 x^{7} - 4320 x^{8} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.17

Subtract $4320 x^{8}$ from $- 3840 x^{8}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 1920 x^{7} + 12960 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.18

Add $1920 x^{7}$ and $12960 x^{7}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 14880 x^{7} - 17280 x^{6} + 8640 x^{5} + 1080 x^{7} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.19

Add $14880 x^{7}$ and $1080 x^{7}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 17280 x^{6} + 8640 x^{5} - 8640 x^{6} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.20

Subtract $8640 x^{6}$ from $- 17280 x^{6}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 8640 x^{5} + 25920 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.21

Add $8640 x^{5}$ and $25920 x^{5}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 34560 x^{5} - 34560 x^{4} + 17280 x^{3} + 810 x^{5} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.22

Add $34560 x^{5}$ and $810 x^{5}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 34560 x^{4} + 17280 x^{3} - 6480 x^{4} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.23

Subtract $6480 x^{4}$ from $- 34560 x^{4}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 17280 x^{3} + 19440 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.24

Add $17280 x^{3}$ and $19440 x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + {(x^{2} + 3)}^{5} (4) {(x - 2)}^{3}$

Step 1.25

Use the Binomial Theorem.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + ({(x^{2})}^{5} + 5 {(x^{2})}^{4} \cdot 3 + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26

Simplify each term.

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Step 1.26.1

Multiply the exponents in ${(x^{2})}^{5}$ .

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Step 1.26.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{2 \cdot 5} + 5 {(x^{2})}^{4} \cdot 3 + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.1.2

Multiply $2$ by $5$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 5 {(x^{2})}^{4} \cdot 3 + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.2

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 1.26.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 5 x^{2 \cdot 4} \cdot 3 + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.2.2

Multiply $2$ by $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 5 x^{8} \cdot 3 + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.3

Multiply $3$ by $5$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 10 {(x^{2})}^{3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.4

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 1.26.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 10 x^{2 \cdot 3} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.4.2

Multiply $2$ by $3$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 10 x^{6} \cdot 3^{2} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.5

Raise $3$ to the power of $2$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 10 x^{6} \cdot 9 + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.6

Multiply $9$ by $10$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 10 {(x^{2})}^{2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.7

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.26.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 10 x^{2 \cdot 2} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.7.2

Multiply $2$ by $2$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 10 x^{4} \cdot 3^{3} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.8

Raise $3$ to the power of $3$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 10 x^{4} \cdot 27 + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.9

Multiply $27$ by $10$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 5 x^{2} \cdot 3^{4} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.10

Raise $3$ to the power of $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 5 x^{2} \cdot 81 + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.11

Multiply $81$ by $5$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 3^{5}) \cdot 4 {(x - 2)}^{3}$

Step 1.26.12

Raise $3$ to the power of $5$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} + 15 x^{8} + 90 x^{6} + 270 x^{4} + 405 x^{2} + 243) \cdot 4 {(x - 2)}^{3}$

Step 1.27

Apply the distributive property.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (x^{10} \cdot 4 + 15 x^{8} \cdot 4 + 90 x^{6} \cdot 4 + 270 x^{4} \cdot 4 + 405 x^{2} \cdot 4 + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28

Simplify.

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Step 1.28.1

Move $4$ to the left of $x^{10}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 15 x^{8} \cdot 4 + 90 x^{6} \cdot 4 + 270 x^{4} \cdot 4 + 405 x^{2} \cdot 4 + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28.2

Multiply $4$ by $15$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 60 x^{8} + 90 x^{6} \cdot 4 + 270 x^{4} \cdot 4 + 405 x^{2} \cdot 4 + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28.3

Multiply $4$ by $90$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 60 x^{8} + 360 x^{6} + 270 x^{4} \cdot 4 + 405 x^{2} \cdot 4 + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28.4

Multiply $4$ by $270$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 60 x^{8} + 360 x^{6} + 1080 x^{4} + 405 x^{2} \cdot 4 + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28.5

Multiply $4$ by $405$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 60 x^{8} + 360 x^{6} + 1080 x^{4} + 1620 x^{2} + 243 \cdot 4) {(x - 2)}^{3}$

Step 1.28.6

Multiply $243$ by $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 \cdot x^{10} + 60 x^{8} + 360 x^{6} + 1080 x^{4} + 1620 x^{2} + 972) {(x - 2)}^{3}$

Step 1.29

Use the Binomial Theorem.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + (4 x^{10} + 60 x^{8} + 360 x^{6} + 1080 x^{4} + 1620 x^{2} + 972) (x^{3} + 3 x^{2} \cdot - 2 + 3 x {(- 2)}^{2} + {(- 2)}^{3})$

Step 1.30

Simplify each term.

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Step 1.30.1

Multiply $- 2$ by $3$ .

Step 1.30.2

Raise $- 2$ to the power of $2$ .

Step 1.30.3

Multiply $4$ by $3$ .

Step 1.30.4

Raise $- 2$ to the power of $3$ .

Step 1.31

Expand $(4 x^{10} + 60 x^{8} + 360 x^{6} + 1080 x^{4} + 1620 x^{2} + 972) (x^{3} - 6 x^{2} + 12 x - 8)$ by multiplying each term in the first expression by each term in the second expression.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{10} x^{3} + 4 x^{10} (- 6 x^{2}) + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32

Simplify each term.

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Step 1.32.1

Multiply $x^{10}$ by $x^{3}$ by adding the exponents.

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Step 1.32.1.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 (x^{3} x^{10}) + 4 x^{10} (- 6 x^{2}) + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{3 + 10} + 4 x^{10} (- 6 x^{2}) + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.1.3

Add $3$ and $10$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} + 4 x^{10} (- 6 x^{2}) + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.2

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} + 4 \cdot - 6 x^{10} x^{2} + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.3

Multiply $x^{10}$ by $x^{2}$ by adding the exponents.

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Step 1.32.3.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} + 4 \cdot - 6 (x^{2} x^{10}) + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} + 4 \cdot - 6 x^{2 + 10} + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.3.3

Add $2$ and $10$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} + 4 \cdot - 6 x^{12} + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.4

Multiply $4$ by $- 6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 x^{10} (12 x) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.5

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 \cdot 12 x^{10} x + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.6

Multiply $x^{10}$ by $x$ by adding the exponents.

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Step 1.32.6.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 \cdot 12 (x \cdot x^{10}) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.6.2

Multiply $x$ by $x^{10}$ .

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Step 1.32.6.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 \cdot 12 (x^{1} x^{10}) + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 \cdot 12 x^{1 + 10} + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.6.3

Add $1$ and $10$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 4 \cdot 12 x^{11} + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.7

Multiply $4$ by $12$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} + 4 x^{10} \cdot - 8 + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.8

Multiply $- 8$ by $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{8} x^{3} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.9

Multiply $x^{8}$ by $x^{3}$ by adding the exponents.

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Step 1.32.9.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 (x^{3} x^{8}) + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.9.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{3 + 8} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.9.3

Add $3$ and $8$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} + 60 x^{8} (- 6 x^{2}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.10

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} + 60 \cdot - 6 x^{8} x^{2} + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.11

Multiply $x^{8}$ by $x^{2}$ by adding the exponents.

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Step 1.32.11.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} + 60 \cdot - 6 (x^{2} x^{8}) + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.11.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} + 60 \cdot - 6 x^{2 + 8} + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.11.3

Add $2$ and $8$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} + 60 \cdot - 6 x^{10} + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.12

Multiply $60$ by $- 6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 x^{8} (12 x) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.13

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 \cdot 12 x^{8} x + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.14

Multiply $x^{8}$ by $x$ by adding the exponents.

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Step 1.32.14.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 \cdot 12 (x \cdot x^{8}) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.14.2

Multiply $x$ by $x^{8}$ .

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Step 1.32.14.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 \cdot 12 (x^{1} x^{8}) + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.14.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 \cdot 12 x^{1 + 8} + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.14.3

Add $1$ and $8$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 60 \cdot 12 x^{9} + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.15

Multiply $60$ by $12$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} + 60 x^{8} \cdot - 8 + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.16

Multiply $- 8$ by $60$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{6} x^{3} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.17

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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Step 1.32.17.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 (x^{3} x^{6}) + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.17.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{3 + 6} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.17.3

Add $3$ and $6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} + 360 x^{6} (- 6 x^{2}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.18

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} + 360 \cdot - 6 x^{6} x^{2} + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.19

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 1.32.19.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} + 360 \cdot - 6 (x^{2} x^{6}) + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.19.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} + 360 \cdot - 6 x^{2 + 6} + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.19.3

Add $2$ and $6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} + 360 \cdot - 6 x^{8} + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.20

Multiply $360$ by $- 6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 x^{6} (12 x) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.21

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 \cdot 12 x^{6} x + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.22

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 1.32.22.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 \cdot 12 (x \cdot x^{6}) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.22.2

Multiply $x$ by $x^{6}$ .

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Step 1.32.22.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 \cdot 12 (x^{1} x^{6}) + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.22.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 \cdot 12 x^{1 + 6} + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.22.3

Add $1$ and $6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 360 \cdot 12 x^{7} + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.23

Multiply $360$ by $12$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} + 360 x^{6} \cdot - 8 + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.24

Multiply $- 8$ by $360$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{4} x^{3} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.25

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 1.32.25.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 (x^{3} x^{4}) + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.25.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{3 + 4} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.25.3

Add $3$ and $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} + 1080 x^{4} (- 6 x^{2}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.26

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} + 1080 \cdot - 6 x^{4} x^{2} + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.27

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 1.32.27.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} + 1080 \cdot - 6 (x^{2} x^{4}) + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.27.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} + 1080 \cdot - 6 x^{2 + 4} + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.27.3

Add $2$ and $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} + 1080 \cdot - 6 x^{6} + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.28

Multiply $1080$ by $- 6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 x^{4} (12 x) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.29

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 \cdot 12 x^{4} x + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.30

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 1.32.30.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 \cdot 12 (x \cdot x^{4}) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.30.2

Multiply $x$ by $x^{4}$ .

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Step 1.32.30.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 \cdot 12 (x^{1} x^{4}) + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.30.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 \cdot 12 x^{1 + 4} + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.30.3

Add $1$ and $4$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 1080 \cdot 12 x^{5} + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.31

Multiply $1080$ by $12$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} + 1080 x^{4} \cdot - 8 + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.32

Multiply $- 8$ by $1080$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{2} x^{3} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.33

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.32.33.1

Move $x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 (x^{3} x^{2}) + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.33.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{3 + 2} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.33.3

Add $3$ and $2$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} + 1620 x^{2} (- 6 x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.34

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} + 1620 \cdot - 6 x^{2} x^{2} + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.35

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.32.35.1

Move $x^{2}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} + 1620 \cdot - 6 (x^{2} x^{2}) + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.35.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} + 1620 \cdot - 6 x^{2 + 2} + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.35.3

Add $2$ and $2$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} + 1620 \cdot - 6 x^{4} + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.36

Multiply $1620$ by $- 6$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 x^{2} (12 x) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.37

Rewrite using the commutative property of multiplication.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 \cdot 12 x^{2} x + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.38

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.32.38.1

Move $x$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 \cdot 12 (x \cdot x^{2}) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.38.2

Multiply $x$ by $x^{2}$ .

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Step 1.32.38.2.1

Raise $x$ to the power of $1$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 \cdot 12 (x^{1} x^{2}) + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.38.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 \cdot 12 x^{1 + 2} + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.38.3

Add $1$ and $2$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 1620 \cdot 12 x^{3} + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.39

Multiply $1620$ by $12$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} + 1620 x^{2} \cdot - 8 + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.40

Multiply $- 8$ by $1620$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} + 972 (- 6 x^{2}) + 972 (12 x) + 972 \cdot - 8$

Step 1.32.41

Multiply $- 6$ by $972$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 972 (12 x) + 972 \cdot - 8$

Step 1.32.42

Multiply $12$ by $972$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x + 972 \cdot - 8$

Step 1.32.43

Multiply $972$ by $- 8$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 48 x^{11} - 32 x^{10} + 60 x^{11} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.33

Add $48 x^{11}$ and $60 x^{11}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 32 x^{10} - 360 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.34

Subtract $360 x^{10}$ from $- 32 x^{10}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 720 x^{9} - 480 x^{8} + 360 x^{9} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.35

Add $720 x^{9}$ and $360 x^{9}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 480 x^{8} - 2160 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.36

Subtract $2160 x^{8}$ from $- 480 x^{8}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 4320 x^{7} - 2880 x^{6} + 1080 x^{7} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.37

Add $4320 x^{7}$ and $1080 x^{7}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 2880 x^{6} - 6480 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.38

Subtract $6480 x^{6}$ from $- 2880 x^{6}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 12960 x^{5} - 8640 x^{4} + 1620 x^{5} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.39

Add $12960 x^{5}$ and $1620 x^{5}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 8640 x^{4} - 9720 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.40

Subtract $9720 x^{4}$ from $- 8640 x^{4}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 19440 x^{3} - 12960 x^{2} + 972 x^{3} - 5832 x^{2} + 11664 x - 7776$

Step 1.41

Add $19440 x^{3}$ and $972 x^{3}$ .

$10 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 4 x^{13} - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 12960 x^{2} - 5832 x^{2} + 11664 x - 7776$

Step 1.42

Subtract $5832 x^{2}$ from $- 12960 x^{2}$ .

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $10 x^{13}$ and $4 x^{13}$ .

$14 x^{13} - 80 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x - 24 x^{12} + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.2

Subtract $24 x^{12}$ from $- 80 x^{12}$ .

$14 x^{13} - 104 x^{12} + 360 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 108 x^{11} - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.3

Add $360 x^{11}$ and $108 x^{11}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1280 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x - 392 x^{10} + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.4

Subtract $392 x^{10}$ from $- 1280 x^{10}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 3580 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 1080 x^{9} - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.5

Add $3580 x^{9}$ and $1080 x^{9}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 8160 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x - 2640 x^{8} + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.6

Subtract $2640 x^{8}$ from $- 8160 x^{8}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 15960 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 5400 x^{7} - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.7

Add $15960 x^{7}$ and $5400 x^{7}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 25920 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x - 9360 x^{6} + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.8

Subtract $9360 x^{6}$ from $- 25920 x^{6}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 35370 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 14580 x^{5} - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.9

Add $35370 x^{5}$ and $14580 x^{5}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 49950 x^{5} - 41040 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x - 18360 x^{4} + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.10

Subtract $18360 x^{4}$ from $- 41040 x^{4}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 49950 x^{5} - 59400 x^{4} + 36720 x^{3} - 25920 x^{2} + 12960 x + 20412 x^{3} - 18792 x^{2} + 11664 x - 7776$

Step 2.11

Add $36720 x^{3}$ and $20412 x^{3}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 49950 x^{5} - 59400 x^{4} + 57132 x^{3} - 25920 x^{2} + 12960 x - 18792 x^{2} + 11664 x - 7776$

Step 2.12

Subtract $18792 x^{2}$ from $- 25920 x^{2}$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 49950 x^{5} - 59400 x^{4} + 57132 x^{3} - 44712 x^{2} + 12960 x + 11664 x - 7776$

Step 2.13

Add $12960 x$ and $11664 x$ .

$14 x^{13} - 104 x^{12} + 468 x^{11} - 1672 x^{10} + 4660 x^{9} - 10800 x^{8} + 21360 x^{7} - 35280 x^{6} + 49950 x^{5} - 59400 x^{4} + 57132 x^{3} - 44712 x^{2} + 24624 x - 7776$