Factor 12x^2-3y^2

$12 x^{2} - 3 y^{2}$

Step 1

Factor $3$ out of $12 x^{2} - 3 y^{2}$ .

Factor $3$ out of $12 x^{2}$ .

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

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

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

Factor $3$ out of $3 (4 x^{2}) + 3 (- y^{2})$ .

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

Step 2

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

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

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 $a = 2 x$ and $b = y$ .

$3 ((2 x + y) (2 x - y))$

Remove unnecessary parentheses.

$3 (2 x + y) (2 x - y)$