Factor 12x^2-147

$12 x^{2} - 147$

Step 1

Factor $3$ out of $12 x^{2} - 147$ .

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

$3 (4 x^{2}) - 147$

Factor $3$ out of $- 147$ .

$3 (4 x^{2}) + 3 (- 49)$

Factor $3$ out of $3 (4 x^{2}) + 3 (- 49)$ .

$3 (4 x^{2} - 49)$

Step 2

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

$3 ({(2 x)}^{2} - 49)$

Step 3

Rewrite $49$ as $7^{2}$ .

$3 ({(2 x)}^{2} - 7^{2})$

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 $a = 2 x$ and $b = 7$ .

$3 ((2 x + 7) (2 x - 7))$

Remove unnecessary parentheses.

$3 (2 x + 7) (2 x - 7)$