Factor by Grouping 18x^2y-24x^2-27y+36

$18 x^{2} y - 24 x^{2} - 27 y + 36$

Step 1

Factor out the GCF of $3$ from $18 x^{2} y - 24 x^{2} - 27 y + 36$ .

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

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

$3 (6 x^{2} y) - 24 x^{2} - 27 y + 36$

Factor out the GCF of $3$ from the expression $- 24 x^{2}$ .

$3 (6 x^{2} y) + 3 (- 8 x^{2}) - 27 y + 36$

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

$3 (6 x^{2} y) + 3 (- 8 x^{2}) + 3 (- 9 y) + 36$

Factor out the GCF of $3$ from the expression $36$ .

$3 (6 x^{2} y) + 3 (- 8 x^{2}) + 3 (- 9 y) + 3 (12)$

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

$3 (6 x^{2} y - 8 x^{2} - 9 y + 12)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((6 x^{2} y - 8 x^{2}) - 9 y + 12)$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 4$ .

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