Factor 81x^2-9

$81 x^{2} - 9$

Step 1

Factor $9$ out of $81 x^{2} - 9$ .

Factor $9$ out of $81 x^{2}$ .

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

Factor $9$ out of $- 9$ .

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

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

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

Step 2

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

$9 ({(3 x)}^{2} - 1)$

Step 3

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

$9 ({(3 x)}^{2} - 1^{2})$

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 $b = 1$ .

$9 ((3 x + 1) (3 x - 1))$

Remove unnecessary parentheses.

$9 (3 x + 1) (3 x - 1)$