Factor 196n^2-144

$196 n^{2} - 144$

Step 1

Factor $4$ out of $196 n^{2} - 144$ .

Factor $4$ out of $196 n^{2}$ .

$4 (49 n^{2}) - 144$

Factor $4$ out of $- 144$ .

$4 (49 n^{2}) + 4 (- 36)$

Factor $4$ out of $4 (49 n^{2}) + 4 (- 36)$ .

$4 (49 n^{2} - 36)$

Step 2

Rewrite $49 n^{2}$ as ${(7 n)}^{2}$ .

$4 ({(7 n)}^{2} - 36)$

Step 3

Rewrite $36$ as $6^{2}$ .

$4 ({(7 n)}^{2} - 6^{2})$

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 $a = 7 n$ and $b = 6$ .

$4 ((7 n + 6) (7 n - 6))$

Remove unnecessary parentheses.

$4 (7 n + 6) (7 n - 6)$