Factor 18x^3-2x

$18 x^{3} - 2 x$

Step 1

Factor $2 x$ out of $18 x^{3} - 2 x$ .

Factor $2 x$ out of $18 x^{3}$ .

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

Factor $2 x$ out of $- 2 x$ .

$2 x (9 x^{2}) + 2 x (- 1)$

Factor $2 x$ out of $2 x (9 x^{2}) + 2 x (- 1)$ .

$2 x (9 x^{2} - 1)$

Step 2

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

$2 x ({(3 x)}^{2} - 1)$

Step 3

Rewrite $1$ as $1^{2}$ .

$2 x ({(3 x)}^{2} - 1^{2})$

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 $a = 3 x$ and $b = 1$ .

$2 x ((3 x + 1) (3 x - 1))$

Remove unnecessary parentheses.

$2 x (3 x + 1) (3 x - 1)$