Factor 12v^2-27

$12 v^{2} - 27$

Step 1

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

Factor $3$ out of $12 v^{2}$ .

$3 (4 v^{2}) - 27$

Factor $3$ out of $- 27$ .

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

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

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

Step 2

Rewrite $4 v^{2}$ as ${(2 v)}^{2}$ .

$3 ({(2 v)}^{2} - 9)$

Step 3

Rewrite $9$ as $3^{2}$ .

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

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

$3 ((2 v + 3) (2 v - 3))$

Remove unnecessary parentheses.

$3 (2 v + 3) (2 v - 3)$