Factor 12x^2y-3y

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

Step 1

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

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

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

Factor $3 y$ out of $- 3 y$ .

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

Factor $3 y$ out of $3 y (4 x^{2}) + 3 y (- 1)$ .

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

Step 2

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

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

Step 3

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

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

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 $a = 2 x$ and $b = 1$ .

$3 y ((2 x + 1) (2 x - 1))$

Remove unnecessary parentheses.

$3 y (2 x + 1) (2 x - 1)$