Factor by Grouping 12x^2y-20x^2-18y+30

$12 x^{2} y - 20 x^{2} - 18 y + 30$

Step 1

Factor out the GCF of $2$ from $12 x^{2} y - 20 x^{2} - 18 y + 30$ .

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

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

$2 (6 x^{2} y) - 20 x^{2} - 18 y + 30$

Factor out the GCF of $2$ from the expression $- 20 x^{2}$ .

$2 (6 x^{2} y) + 2 (- 10 x^{2}) - 18 y + 30$

Factor out the GCF of $2$ from the expression $- 18 y$ .

$2 (6 x^{2} y) + 2 (- 10 x^{2}) + 2 (- 9 y) + 30$

Factor out the GCF of $2$ from the expression $30$ .

$2 (6 x^{2} y) + 2 (- 10 x^{2}) + 2 (- 9 y) + 2 (15)$

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

$2 (6 x^{2} y - 10 x^{2} - 9 y + 15)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((6 x^{2} y - 10 x^{2}) - 9 y + 15)$

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

$2 (2 x^{2} (3 y - 5) - 3 (3 y - 5))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 5$ .

$2 ((3 y - 5) (2 x^{2} - 3))$