Factor 27r^2-12

$27 r^{2} - 12$

Step 1

Factor $3$ out of $27 r^{2} - 12$ .

Factor $3$ out of $27 r^{2}$ .

$3 (9 r^{2}) - 12$

Factor $3$ out of $- 12$ .

$3 (9 r^{2}) + 3 (- 4)$

Factor $3$ out of $3 (9 r^{2}) + 3 (- 4)$ .

$3 (9 r^{2} - 4)$

Step 2

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

$3 ({(3 r)}^{2} - 4)$

Step 3

Rewrite $4$ as $2^{2}$ .

$3 ({(3 r)}^{2} - 2^{2})$

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 $a = 3 r$ and $b = 2$ .

$3 ((3 r + 2) (3 r - 2))$

Remove unnecessary parentheses.

$3 (3 r + 2) (3 r - 2)$