Factor by Grouping 8x^2y-28x^2-12y+42

$8 x^{2} y - 28 x^{2} - 12 y + 42$

Step 1

Factor out the GCF of $2$ from $8 x^{2} y - 28 x^{2} - 12 y + 42$ .

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

Factor out the GCF of $2$ from the expression $8 x^{2} y$ .

$2 (4 x^{2} y) - 28 x^{2} - 12 y + 42$

Factor out the GCF of $2$ from the expression $- 28 x^{2}$ .

$2 (4 x^{2} y) + 2 (- 14 x^{2}) - 12 y + 42$

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

$2 (4 x^{2} y) + 2 (- 14 x^{2}) + 2 (- 6 y) + 42$

Factor out the GCF of $2$ from the expression $42$ .

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

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

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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