Factor by Grouping 12x^2y-18x^2-8y+12

$12 x^{2} y - 18 x^{2} - 8 y + 12$

Step 1

Factor out the GCF of $2$ from $12 x^{2} y - 18 x^{2} - 8 y + 12$ .

Factor out the GCF of $2$ from each term in the polynomial.

Factor out the GCF of $2$ from the expression $12 x^{2} y$ .

$2 (6 x^{2} y) - 18 x^{2} - 8 y + 12$

Factor out the GCF of $2$ from the expression $- 18 x^{2}$ .

$2 (6 x^{2} y) + 2 (- 9 x^{2}) - 8 y + 12$

Factor out the GCF of $2$ from the expression $- 8 y$ .

$2 (6 x^{2} y) + 2 (- 9 x^{2}) + 2 (- 4 y) + 12$

Factor out the GCF of $2$ from the expression $12$ .

$2 (6 x^{2} y) + 2 (- 9 x^{2}) + 2 (- 4 y) + 2 (6)$

Since all the terms share a common factor of $2$ , it can be factored out of each term.

$2 (6 x^{2} y - 9 x^{2} - 4 y + 6)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((6 x^{2} y - 9 x^{2}) - 4 y + 6)$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y - 3$ .

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