Factor 2x^2-18y^2

$2 x^{2} - 18 y^{2}$

Step 1

Factor $2$ out of $2 x^{2} - 18 y^{2}$ .

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

$2 (x^{2}) - 18 y^{2}$

Factor $2$ out of $- 18 y^{2}$ .

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

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

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

Step 2

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

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

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 $b = 3 y$ .

$2 ((x + 3 y) (x - (3 y)))$

Step 4

Factor.

Multiply $3$ by $- 1$ .

$2 ((x + 3 y) (x - 3 y))$

Remove unnecessary parentheses.

$2 (x + 3 y) (x - 3 y)$