Factor 9x^2y+12y-9x^2-12

$9 x^{2} y + 12 y - 9 x^{2} - 12$

Step 1

Factor $3$ out of $9 x^{2} y + 12 y - 9 x^{2} - 12$ .

Factor $3$ out of $9 x^{2} y$ .

$3 (3 x^{2} y) + 12 y - 9 x^{2} - 12$

Factor $3$ out of $12 y$ .

$3 (3 x^{2} y) + 3 (4 y) - 9 x^{2} - 12$

Factor $3$ out of $- 9 x^{2}$ .

$3 (3 x^{2} y) + 3 (4 y) + 3 (- 3 x^{2}) - 12$

Factor $3$ out of $- 12$ .

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

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

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

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

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

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

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $3 x^{2} + 4$ .

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

Remove unnecessary parentheses.

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