Factor 8x^3-72xy^2

$8 x^{3} - 72 x y^{2}$

Step 1

Factor $8 x$ out of $8 x^{3} - 72 x y^{2}$ .

Factor $8 x$ out of $8 x^{3}$ .

$8 x (x^{2}) - 72 x y^{2}$

Factor $8 x$ out of $- 72 x y^{2}$ .

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

Factor $8 x$ out of $8 x (x^{2}) + 8 x (- 9 y^{2})$ .

$8 x (x^{2} - 9 y^{2})$

Step 2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

$8 x (x^{2} - {(3 y)}^{2})$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3 y$ .

$8 x ((x + 3 y) (x - (3 y)))$

Step 4

Factor.

Multiply $3$ by $- 1$ .

$8 x ((x + 3 y) (x - 3 y))$

Remove unnecessary parentheses.

$8 x (x + 3 y) (x - 3 y)$