Factor by Grouping 18x^2y-63x^2-12y+42

$18 x^{2} y - 63 x^{2} - 12 y + 42$

Step 1

Factor out the GCF of $3$ from $18 x^{2} y - 63 x^{2} - 12 y + 42$ .

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

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

$3 (6 x^{2} y) - 63 x^{2} - 12 y + 42$

Factor out the GCF of $3$ from the expression $- 63 x^{2}$ .

$3 (6 x^{2} y) + 3 (- 21 x^{2}) - 12 y + 42$

Factor out the GCF of $3$ from the expression $- 12 y$ .

$3 (6 x^{2} y) + 3 (- 21 x^{2}) + 3 (- 4 y) + 42$

Factor out the GCF of $3$ from the expression $42$ .

$3 (6 x^{2} y) + 3 (- 21 x^{2}) + 3 (- 4 y) + 3 (14)$

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

$3 (6 x^{2} y - 21 x^{2} - 4 y + 14)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((6 x^{2} y - 21 x^{2}) - 4 y + 14)$

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

$3 (3 x^{2} (2 y - 7) - 2 (2 y - 7))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 y - 7$ .

$3 ((2 y - 7) (3 x^{2} - 2))$