Factor by Grouping 12x^2y-18x^2-18y+27

$12 x^{2} y - 18 x^{2} - 18 y + 27$

Step 1

Factor out the GCF of $3$ from $12 x^{2} y - 18 x^{2} - 18 y + 27$ .

Factor out the GCF of $3$ from each term in the polynomial.

Factor out the GCF of $3$ from the expression $12 x^{2} y$ .

$3 (4 x^{2} y) - 18 x^{2} - 18 y + 27$

Factor out the GCF of $3$ from the expression $- 18 x^{2}$ .

$3 (4 x^{2} y) + 3 (- 6 x^{2}) - 18 y + 27$

Factor out the GCF of $3$ from the expression $- 18 y$ .

$3 (4 x^{2} y) + 3 (- 6 x^{2}) + 3 (- 6 y) + 27$

Factor out the GCF of $3$ from the expression $27$ .

$3 (4 x^{2} y) + 3 (- 6 x^{2}) + 3 (- 6 y) + 3 (9)$

Since all the terms share a common factor of $3$ , it can be factored out of each term.

$3 (4 x^{2} y - 6 x^{2} - 6 y + 9)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((4 x^{2} y - 6 x^{2}) - 6 y + 9)$

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

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

Step 3

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

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