Algebra Examples

$2 x^{4} - 32$

Step 1

Factor $2$ out of $2 x^{4} - 32$ .

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Step 1.1

Factor $2$ out of $2 x^{4}$ .

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

Step 1.2

Factor $2$ out of $- 32$ .

$2 x^{4} + 2 \cdot - 16$

Step 1.3

Factor $2$ out of $2 x^{4} + 2 \cdot - 16$ .

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

Step 2

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

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

Step 3

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

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

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 $b = 4$ .

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

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

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 $b = 2$ .

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

Step 5.1.2.2

Remove unnecessary parentheses.

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

Step 5.2

Remove unnecessary parentheses.

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