Factor 48y^4-3y^2

$48 y^{4} - 3 y^{2}$

Step 1

Factor $3 y^{2}$ out of $48 y^{4} - 3 y^{2}$ .

Factor $3 y^{2}$ out of $48 y^{4}$ .

$3 y^{2} (16 y^{2}) - 3 y^{2}$

Factor $3 y^{2}$ out of $- 3 y^{2}$ .

$3 y^{2} (16 y^{2}) + 3 y^{2} (- 1)$

Factor $3 y^{2}$ out of $3 y^{2} (16 y^{2}) + 3 y^{2} (- 1)$ .

$3 y^{2} (16 y^{2} - 1)$

Step 2

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

$3 y^{2} ({(4 y)}^{2} - 1)$

Step 3

Rewrite $1$ as $1^{2}$ .

$3 y^{2} ({(4 y)}^{2} - 1^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 y$ and $b = 1$ .

$3 y^{2} ((4 y + 1) (4 y - 1))$

Remove unnecessary parentheses.

$3 y^{2} (4 y + 1) (4 y - 1)$