Algebra Examples

$2 x^{3} (4 x^{3} - 6 x + 4) + 9 x (3 x^{5} - 6 x^{3} + 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.2.3

Multiply $4$ by $2$ .

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

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x^{3}$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Add $3$ and $3$ .

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

Step 1.3.2

Multiply $2$ by $4$ .

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

Step 1.3.3

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

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Step 1.3.3.1

Move $x$ .

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

Step 1.3.3.2

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

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Step 1.3.3.2.1

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

$8 x^{6} + 2 \cdot - 6 (x^{1} x^{3}) + 8 x^{3} + 9 x (3 x^{5} - 6 x^{3} + 5)$

Step 1.3.3.2.2

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

$8 x^{6} + 2 \cdot - 6 x^{1 + 3} + 8 x^{3} + 9 x (3 x^{5} - 6 x^{3} + 5)$

Step 1.3.3.3

Add $1$ and $3$ .

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

Step 1.3.4

Multiply $2$ by $- 6$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

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

Step 1.5.2

Rewrite using the commutative property of multiplication.

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

Step 1.5.3

Multiply $5$ by $9$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 9 \cdot 3 x \cdot x^{5} + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6

Simplify each term.

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Step 1.6.1

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

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Step 1.6.1.1

Move $x^{5}$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 9 \cdot 3 (x^{5} x) + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6.1.2

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

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Step 1.6.1.2.1

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

$8 x^{6} - 12 x^{4} + 8 x^{3} + 9 \cdot 3 (x^{5} x^{1}) + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6.1.2.2

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

$8 x^{6} - 12 x^{4} + 8 x^{3} + 9 \cdot 3 x^{5 + 1} + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6.1.3

Add $5$ and $1$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 9 \cdot 3 x^{6} + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6.2

Multiply $9$ by $3$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} + 9 \cdot - 6 x \cdot x^{3} + 45 x$

Step 1.6.3

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

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Step 1.6.3.1

Move $x^{3}$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} + 9 \cdot - 6 (x^{3} x) + 45 x$

Step 1.6.3.2

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

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Step 1.6.3.2.1

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

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} + 9 \cdot - 6 (x^{3} x^{1}) + 45 x$

Step 1.6.3.2.2

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

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} + 9 \cdot - 6 x^{3 + 1} + 45 x$

Step 1.6.3.3

Add $3$ and $1$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} + 9 \cdot - 6 x^{4} + 45 x$

Step 1.6.4

Multiply $9$ by $- 6$ .

$8 x^{6} - 12 x^{4} + 8 x^{3} + 27 x^{6} - 54 x^{4} + 45 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 x^{6}$ and $27 x^{6}$ .

$35 x^{6} - 12 x^{4} + 8 x^{3} - 54 x^{4} + 45 x$

Step 2.2

Subtract $54 x^{4}$ from $- 12 x^{4}$ .

$35 x^{6} - 66 x^{4} + 8 x^{3} + 45 x$