Factor 16x^4-256x^2

$16 x^{4} - 256 x^{2}$

Step 1

Factor $16 x^{2}$ out of $16 x^{4} - 256 x^{2}$ .

Factor $16 x^{2}$ out of $16 x^{4}$ .

$16 x^{2} (x^{2}) - 256 x^{2}$

Factor $16 x^{2}$ out of $- 256 x^{2}$ .

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

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

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

Step 2

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

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

Step 3

Factor.

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 $b = 4$ .

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

Remove unnecessary parentheses.

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