Factor 2w^4-32

$2 w^{4} - 32$

Step 1

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

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

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

Factor $2$ out of $- 32$ .

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

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Factor.

Simplify.

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

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

Factor.

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

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor 2w^4-32

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