Factor 16x^2-100

$16 x^{2} - 100$

Step 1

Factor $4$ out of $16 x^{2} - 100$ .

Factor $4$ out of $16 x^{2}$ .

$4 (4 x^{2}) - 100$

Factor $4$ out of $- 100$ .

$4 (4 x^{2}) + 4 (- 25)$

Factor $4$ out of $4 (4 x^{2}) + 4 (- 25)$ .

$4 (4 x^{2} - 25)$

Step 2

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

$4 ({(2 x)}^{2} - 25)$

Step 3

Rewrite $25$ as $5^{2}$ .

$4 ({(2 x)}^{2} - 5^{2})$

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 $b = 5$ .

$4 ((2 x + 5) (2 x - 5))$

Remove unnecessary parentheses.

$4 (2 x + 5) (2 x - 5)$