Finite Math Examples

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

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the product rule to $2 x$ .

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

Step 1.2.2

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

$(16 x^{4} + 4 {(2 x)}^{3} \cdot 3 + 6 {(2 x)}^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.3

Apply the product rule to $2 x$ .

$(16 x^{4} + 4 (2^{3} x^{3}) \cdot 3 + 6 {(2 x)}^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.4

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

$(16 x^{4} + 4 (8 x^{3}) \cdot 3 + 6 {(2 x)}^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.5

Multiply $8$ by $4$ .

$(16 x^{4} + 32 x^{3} \cdot 3 + 6 {(2 x)}^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.6

Multiply $3$ by $32$ .

$(16 x^{4} + 96 x^{3} + 6 {(2 x)}^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.7

Apply the product rule to $2 x$ .

$(16 x^{4} + 96 x^{3} + 6 (2^{2} x^{2}) \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.8

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

$(16 x^{4} + 96 x^{3} + 6 (4 x^{2}) \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.9

Multiply $4$ by $6$ .

$(16 x^{4} + 96 x^{3} + 24 x^{2} \cdot 3^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.10

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

$(16 x^{4} + 96 x^{3} + 24 x^{2} \cdot 9 + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.11

Multiply $9$ by $24$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 4 (2 x) \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.12

Multiply $2$ by $4$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 8 x \cdot 3^{3} + 3^{4}) {(x - 5)}^{5}$

Step 1.2.13

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

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 8 x \cdot 27 + 3^{4}) {(x - 5)}^{5}$

Step 1.2.14

Multiply $27$ by $8$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 3^{4}) {(x - 5)}^{5}$

Step 1.2.15

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

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) {(x - 5)}^{5}$

Step 1.3

Use the Binomial Theorem.

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} + 5 x^{4} \cdot - 5 + 10 x^{3} {(- 5)}^{2} + 10 x^{2} {(- 5)}^{3} + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $- 5$ by $5$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 10 x^{3} {(- 5)}^{2} + 10 x^{2} {(- 5)}^{3} + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4.2

Raise $- 5$ to the power of $2$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 10 x^{3} \cdot 25 + 10 x^{2} {(- 5)}^{3} + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4.3

Multiply $25$ by $10$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} + 10 x^{2} {(- 5)}^{3} + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4.4

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

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} + 10 x^{2} \cdot - 125 + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4.5

Multiply $- 125$ by $10$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} - 1250 x^{2} + 5 x {(- 5)}^{4} + {(- 5)}^{5})$

Step 1.4.6

Raise $- 5$ to the power of $4$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} - 1250 x^{2} + 5 x \cdot 625 + {(- 5)}^{5})$

Step 1.4.7

Multiply $625$ by $5$ .

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} - 1250 x^{2} + 3125 x + {(- 5)}^{5})$

Step 1.4.8

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

$(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} - 1250 x^{2} + 3125 x - 3125)$

Step 1.5

Expand $(16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81) (x^{5} - 25 x^{4} + 250 x^{3} - 1250 x^{2} + 3125 x - 3125)$ by multiplying each term in the first expression by each term in the second expression.

$16 x^{4} x^{5} + 16 x^{4} (- 25 x^{4}) + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6

Simplify terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

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

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Step 1.6.1.1.1

Move $x^{5}$ .

$16 (x^{5} x^{4}) + 16 x^{4} (- 25 x^{4}) + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.1.2

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

$16 x^{5 + 4} + 16 x^{4} (- 25 x^{4}) + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.1.3

Add $5$ and $4$ .

$16 x^{9} + 16 x^{4} (- 25 x^{4}) + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.2

Rewrite using the commutative property of multiplication.

$16 x^{9} + 16 \cdot - 25 x^{4} x^{4} + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.3

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

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Step 1.6.1.3.1

Move $x^{4}$ .

$16 x^{9} + 16 \cdot - 25 (x^{4} x^{4}) + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.3.2

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

$16 x^{9} + 16 \cdot - 25 x^{4 + 4} + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.3.3

Add $4$ and $4$ .

$16 x^{9} + 16 \cdot - 25 x^{8} + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.4

Multiply $16$ by $- 25$ .

$16 x^{9} - 400 x^{8} + 16 x^{4} (250 x^{3}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.5

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 16 \cdot 250 x^{4} x^{3} + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.6

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

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Step 1.6.1.6.1

Move $x^{3}$ .

$16 x^{9} - 400 x^{8} + 16 \cdot 250 (x^{3} x^{4}) + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.6.2

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

$16 x^{9} - 400 x^{8} + 16 \cdot 250 x^{3 + 4} + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.6.3

Add $3$ and $4$ .

$16 x^{9} - 400 x^{8} + 16 \cdot 250 x^{7} + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.7

Multiply $16$ by $250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} + 16 x^{4} (- 1250 x^{2}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.8

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} + 16 \cdot - 1250 x^{4} x^{2} + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.9

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

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Step 1.6.1.9.1

Move $x^{2}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} + 16 \cdot - 1250 (x^{2} x^{4}) + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.9.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} + 16 \cdot - 1250 x^{2 + 4} + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.9.3

Add $2$ and $4$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} + 16 \cdot - 1250 x^{6} + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.10

Multiply $16$ by $- 1250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 x^{4} (3125 x) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.11

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 \cdot 3125 x^{4} x + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.12

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

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Step 1.6.1.12.1

Move $x$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 \cdot 3125 (x \cdot x^{4}) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.12.2

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

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Step 1.6.1.12.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 \cdot 3125 (x^{1} x^{4}) + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.12.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 \cdot 3125 x^{1 + 4} + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.12.3

Add $1$ and $4$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 16 \cdot 3125 x^{5} + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.13

Multiply $16$ by $3125$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} + 16 x^{4} \cdot - 3125 + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.14

Multiply $- 3125$ by $16$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{3} x^{5} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.15

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

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Step 1.6.1.15.1

Move $x^{5}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 (x^{5} x^{3}) + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.15.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{5 + 3} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.15.3

Add $5$ and $3$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} + 96 x^{3} (- 25 x^{4}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.16

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} + 96 \cdot - 25 x^{3} x^{4} + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.17

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

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Step 1.6.1.17.1

Move $x^{4}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} + 96 \cdot - 25 (x^{4} x^{3}) + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.17.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} + 96 \cdot - 25 x^{4 + 3} + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.17.3

Add $4$ and $3$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} + 96 \cdot - 25 x^{7} + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.18

Multiply $96$ by $- 25$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 96 x^{3} (250 x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.19

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 96 \cdot 250 x^{3} x^{3} + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.20

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

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Step 1.6.1.20.1

Move $x^{3}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 96 \cdot 250 (x^{3} x^{3}) + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.20.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 96 \cdot 250 x^{3 + 3} + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.20.3

Add $3$ and $3$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 96 \cdot 250 x^{6} + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.21

Multiply $96$ by $250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} + 96 x^{3} (- 1250 x^{2}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.22

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} + 96 \cdot - 1250 x^{3} x^{2} + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.23

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

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Step 1.6.1.23.1

Move $x^{2}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} + 96 \cdot - 1250 (x^{2} x^{3}) + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.23.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} + 96 \cdot - 1250 x^{2 + 3} + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.23.3

Add $2$ and $3$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} + 96 \cdot - 1250 x^{5} + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.24

Multiply $96$ by $- 1250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 x^{3} (3125 x) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.25

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 \cdot 3125 x^{3} x + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.26

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

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Step 1.6.1.26.1

Move $x$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 \cdot 3125 (x \cdot x^{3}) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.26.2

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

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Step 1.6.1.26.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 \cdot 3125 (x^{1} x^{3}) + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.26.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 \cdot 3125 x^{1 + 3} + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.26.3

Add $1$ and $3$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 96 \cdot 3125 x^{4} + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.27

Multiply $96$ by $3125$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} + 96 x^{3} \cdot - 3125 + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.28

Multiply $- 3125$ by $96$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{2} x^{5} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.29

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

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Step 1.6.1.29.1

Move $x^{5}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 (x^{5} x^{2}) + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.29.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{5 + 2} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.29.3

Add $5$ and $2$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} + 216 x^{2} (- 25 x^{4}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.30

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} + 216 \cdot - 25 x^{2} x^{4} + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.31

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

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Step 1.6.1.31.1

Move $x^{4}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} + 216 \cdot - 25 (x^{4} x^{2}) + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.31.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} + 216 \cdot - 25 x^{4 + 2} + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.31.3

Add $4$ and $2$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} + 216 \cdot - 25 x^{6} + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.32

Multiply $216$ by $- 25$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 216 x^{2} (250 x^{3}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.33

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 216 \cdot 250 x^{2} x^{3} + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.34

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

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Step 1.6.1.34.1

Move $x^{3}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 216 \cdot 250 (x^{3} x^{2}) + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.34.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 216 \cdot 250 x^{3 + 2} + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.34.3

Add $3$ and $2$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 216 \cdot 250 x^{5} + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.35

Multiply $216$ by $250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} + 216 x^{2} (- 1250 x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.36

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} + 216 \cdot - 1250 x^{2} x^{2} + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.37

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

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Step 1.6.1.37.1

Move $x^{2}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} + 216 \cdot - 1250 (x^{2} x^{2}) + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.37.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} + 216 \cdot - 1250 x^{2 + 2} + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.37.3

Add $2$ and $2$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} + 216 \cdot - 1250 x^{4} + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.38

Multiply $216$ by $- 1250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 x^{2} (3125 x) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.39

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 \cdot 3125 x^{2} x + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.40

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

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Step 1.6.1.40.1

Move $x$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 \cdot 3125 (x \cdot x^{2}) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.40.2

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

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Step 1.6.1.40.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 \cdot 3125 (x^{1} x^{2}) + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.40.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 \cdot 3125 x^{1 + 2} + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.40.3

Add $1$ and $2$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 216 \cdot 3125 x^{3} + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.41

Multiply $216$ by $3125$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{2} \cdot - 3125 + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.42

Multiply $- 3125$ by $216$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x \cdot x^{5} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.43

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

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Step 1.6.1.43.1

Move $x^{5}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 (x^{5} x) + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.43.2

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

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Step 1.6.1.43.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 (x^{5} x^{1}) + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.43.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{5 + 1} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.43.3

Add $5$ and $1$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 x (- 25 x^{4}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.44

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 \cdot - 25 x \cdot x^{4} + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.45

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

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Step 1.6.1.45.1

Move $x^{4}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 \cdot - 25 (x^{4} x) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.45.2

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

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Step 1.6.1.45.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 \cdot - 25 (x^{4} x^{1}) + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.45.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 \cdot - 25 x^{4 + 1} + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.45.3

Add $4$ and $1$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} + 216 \cdot - 25 x^{5} + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.46

Multiply $216$ by $- 25$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 x (250 x^{3}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.47

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 \cdot 250 x \cdot x^{3} + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.48

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

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Step 1.6.1.48.1

Move $x^{3}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 \cdot 250 (x^{3} x) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.48.2

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

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Step 1.6.1.48.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 \cdot 250 (x^{3} x^{1}) + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.48.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 \cdot 250 x^{3 + 1} + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.48.3

Add $3$ and $1$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 216 \cdot 250 x^{4} + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.49

Multiply $216$ by $250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 x (- 1250 x^{2}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.50

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 \cdot - 1250 x \cdot x^{2} + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.51

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

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Step 1.6.1.51.1

Move $x^{2}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 \cdot - 1250 (x^{2} x) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.51.2

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

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Step 1.6.1.51.2.1

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 \cdot - 1250 (x^{2} x^{1}) + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.51.2.2

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

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 \cdot - 1250 x^{2 + 1} + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.51.3

Add $2$ and $1$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} + 216 \cdot - 1250 x^{3} + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.52

Multiply $216$ by $- 1250$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 216 x (3125 x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.53

Rewrite using the commutative property of multiplication.

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 216 \cdot 3125 x \cdot x + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.54

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

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Step 1.6.1.54.1

Move $x$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 216 \cdot 3125 (x \cdot x) + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.54.2

Multiply $x$ by $x$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 216 \cdot 3125 x^{2} + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.55

Multiply $216$ by $3125$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} + 216 x \cdot - 3125 + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.56

Multiply $- 3125$ by $216$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} + 81 (- 25 x^{4}) + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.57

Multiply $- 25$ by $81$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 81 (250 x^{3}) + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.58

Multiply $250$ by $81$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} + 81 (- 1250 x^{2}) + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.59

Multiply $- 1250$ by $81$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 81 (3125 x) + 81 \cdot - 3125$

Step 1.6.1.60

Multiply $3125$ by $81$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x + 81 \cdot - 3125$

Step 1.6.1.61

Multiply $81$ by $- 3125$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2

Simplify by adding terms.

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Step 1.6.2.1

Combine the opposite terms in $16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 675000 x^{2} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 675000 x^{2} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$ .

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Step 1.6.2.1.1

Add $- 675000 x^{2}$ and $675000 x^{2}$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} + 0 - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.1.2

Add $16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3}$ and $0$ .

$16 x^{9} - 400 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 96 x^{8} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.2

Add $- 400 x^{8}$ and $96 x^{8}$ .

$16 x^{9} - 304 x^{8} + 4000 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} - 2400 x^{7} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.3

Subtract $2400 x^{7}$ from $4000 x^{7}$ .

$16 x^{9} - 304 x^{8} + 1600 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 216 x^{7} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.4

Add $1600 x^{7}$ and $216 x^{7}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 20000 x^{6} + 50000 x^{5} - 50000 x^{4} + 24000 x^{6} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.5

Add $- 20000 x^{6}$ and $24000 x^{6}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} + 4000 x^{6} + 50000 x^{5} - 50000 x^{4} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} - 5400 x^{6} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.6

Subtract $5400 x^{6}$ from $4000 x^{6}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1400 x^{6} + 50000 x^{5} - 50000 x^{4} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} + 216 x^{6} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.7

Add $- 1400 x^{6}$ and $216 x^{6}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} + 50000 x^{5} - 50000 x^{4} - 120000 x^{5} + 300000 x^{4} - 300000 x^{3} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.8

Subtract $120000 x^{5}$ from $50000 x^{5}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 70000 x^{5} - 50000 x^{4} + 300000 x^{4} - 300000 x^{3} + 54000 x^{5} - 270000 x^{4} + 675000 x^{3} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.9

Add $- 70000 x^{5}$ and $54000 x^{5}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 16000 x^{5} - 50000 x^{4} + 300000 x^{4} - 300000 x^{3} - 270000 x^{4} + 675000 x^{3} - 5400 x^{5} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.10

Subtract $5400 x^{5}$ from $- 16000 x^{5}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21400 x^{5} - 50000 x^{4} + 300000 x^{4} - 300000 x^{3} - 270000 x^{4} + 675000 x^{3} + 54000 x^{4} - 270000 x^{3} - 675000 x + 81 x^{5} - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.11

Add $- 21400 x^{5}$ and $81 x^{5}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} - 50000 x^{4} + 300000 x^{4} - 300000 x^{3} - 270000 x^{4} + 675000 x^{3} + 54000 x^{4} - 270000 x^{3} - 675000 x - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.12

Add $- 50000 x^{4}$ and $300000 x^{4}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 250000 x^{4} - 300000 x^{3} - 270000 x^{4} + 675000 x^{3} + 54000 x^{4} - 270000 x^{3} - 675000 x - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.13

Subtract $270000 x^{4}$ from $250000 x^{4}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} - 20000 x^{4} - 300000 x^{3} + 675000 x^{3} + 54000 x^{4} - 270000 x^{3} - 675000 x - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.14

Add $- 20000 x^{4}$ and $54000 x^{4}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 34000 x^{4} - 300000 x^{3} + 675000 x^{3} - 270000 x^{3} - 675000 x - 2025 x^{4} + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.15

Subtract $2025 x^{4}$ from $34000 x^{4}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 31975 x^{4} - 300000 x^{3} + 675000 x^{3} - 270000 x^{3} - 675000 x + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.16

Add $- 300000 x^{3}$ and $675000 x^{3}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 31975 x^{4} + 375000 x^{3} - 270000 x^{3} - 675000 x + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.17

Subtract $270000 x^{3}$ from $375000 x^{3}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 31975 x^{4} + 105000 x^{3} - 675000 x + 20250 x^{3} - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.18

Add $105000 x^{3}$ and $20250 x^{3}$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 31975 x^{4} + 125250 x^{3} - 675000 x - 101250 x^{2} + 253125 x - 253125$

Step 1.6.2.19

Add $- 675000 x$ and $253125 x$ .

$16 x^{9} - 304 x^{8} + 1816 x^{7} - 1184 x^{6} - 21319 x^{5} + 31975 x^{4} + 125250 x^{3} - 101250 x^{2} - 421875 x - 253125$

Step 2

The largest exponent is the degree of the polynomial.

$9$