Algebra Examples

$2 x^{7} - 32 x^{3}$

Step 1

Factor $2 x^{3}$ out of $2 x^{7} - 32 x^{3}$ .

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Step 1.1

Factor $2 x^{3}$ out of $2 x^{7}$ .

$2 x^{3} (x^{4}) - 32 x^{3}$

Step 1.2

Factor $2 x^{3}$ out of $- 32 x^{3}$ .

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

Step 1.3

Factor $2 x^{3}$ out of $2 x^{3} (x^{4}) + 2 x^{3} (- 16)$ .

$2 x^{3} (x^{4} - 16)$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$2 x^{3} ({(x^{2})}^{2} - 16)$

Step 3

Rewrite $16$ as $4^{2}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 4$ .

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Rewrite $4$ as $2^{2}$ .

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

Step 5.1.2

Factor.

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Step 5.1.2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Step 5.1.2.2

Remove unnecessary parentheses.

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

Step 5.2

Remove unnecessary parentheses.

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