Factor 5x^4-20x^2

$5 x^{4} - 20 x^{2}$

Step 1

Factor $5 x^{2}$ out of $5 x^{4} - 20 x^{2}$ .

Factor $5 x^{2}$ out of $5 x^{4}$ .

$5 x^{2} (x^{2}) - 20 x^{2}$

Factor $5 x^{2}$ out of $- 20 x^{2}$ .

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

Factor $5 x^{2}$ out of $5 x^{2} (x^{2}) + 5 x^{2} (- 4)$ .

$5 x^{2} (x^{2} - 4)$

Step 2

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

$5 x^{2} (x^{2} - 2^{2})$

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 $b = 2$ .

$5 x^{2} ((x + 2) (x - 2))$

Remove unnecessary parentheses.

$5 x^{2} (x + 2) (x - 2)$