Factor 6w^4-54w^2

$6 w^{4} - 54 w^{2}$

Step 1

Factor $6 w^{2}$ out of $6 w^{4} - 54 w^{2}$ .

Factor $6 w^{2}$ out of $6 w^{4}$ .

$6 w^{2} (w^{2}) - 54 w^{2}$

Factor $6 w^{2}$ out of $- 54 w^{2}$ .

$6 w^{2} (w^{2}) + 6 w^{2} (- 9)$

Factor $6 w^{2}$ out of $6 w^{2} (w^{2}) + 6 w^{2} (- 9)$ .

$6 w^{2} (w^{2} - 9)$

Step 2

Rewrite $9$ as $3^{2}$ .

$6 w^{2} (w^{2} - 3^{2})$

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 $a = w$ and $b = 3$ .

$6 w^{2} ((w + 3) (w - 3))$

Remove unnecessary parentheses.

$6 w^{2} (w + 3) (w - 3)$