Factor 5x^2y^3-180y

$5 x^{2} y^{3} - 180 y$

Step 1

Factor $5 y$ out of $5 x^{2} y^{3} - 180 y$ .

Factor $5 y$ out of $5 x^{2} y^{3}$ .

$5 y (x^{2} y^{2}) - 180 y$

Factor $5 y$ out of $- 180 y$ .

$5 y (x^{2} y^{2}) + 5 y (- 36)$

Factor $5 y$ out of $5 y (x^{2} y^{2}) + 5 y (- 36)$ .

$5 y (x^{2} y^{2} - 36)$

Step 2

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$5 y ({(x y)}^{2} - 36)$

Step 3

Rewrite $36$ as $6^{2}$ .

$5 y ({(x y)}^{2} - 6^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x y$ and $b = 6$ .

$5 y ((x y + 6) (x y - 6))$

Remove unnecessary parentheses.

$5 y (x y + 6) (x y - 6)$