Factor 4x^2y+24x^2-24y-144

$4 x^{2} y + 24 x^{2} - 24 y - 144$

Step 1

Factor $4$ out of $4 x^{2} y + 24 x^{2} - 24 y - 144$ .

Factor $4$ out of $4 x^{2} y$ .

$4 (x^{2} y) + 24 x^{2} - 24 y - 144$

Factor $4$ out of $24 x^{2}$ .

$4 (x^{2} y) + 4 (6 x^{2}) - 24 y - 144$

Factor $4$ out of $- 24 y$ .

$4 (x^{2} y) + 4 (6 x^{2}) + 4 (- 6 y) - 144$

Factor $4$ out of $- 144$ .

$4 (x^{2} y) + 4 (6 x^{2}) + 4 (- 6 y) + 4 \cdot - 36$

Factor $4$ out of $4 (x^{2} y) + 4 (6 x^{2})$ .

$4 (x^{2} y + 6 x^{2}) + 4 (- 6 y) + 4 \cdot - 36$

Factor $4$ out of $4 (x^{2} y + 6 x^{2}) + 4 (- 6 y)$ .

$4 (x^{2} y + 6 x^{2} - 6 y) + 4 \cdot - 36$

Factor $4$ out of $4 (x^{2} y + 6 x^{2} - 6 y) + 4 \cdot - 36$ .

$4 (x^{2} y + 6 x^{2} - 6 y - 36)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((x^{2} y + 6 x^{2}) - 6 y - 36)$

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

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

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $y + 6$ .

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

Remove unnecessary parentheses.

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