Factor 48x^2-75

$48 x^{2} - 75$

Step 1

Factor $3$ out of $48 x^{2} - 75$ .

Factor $3$ out of $48 x^{2}$ .

$3 (16 x^{2}) - 75$

Factor $3$ out of $- 75$ .

$3 (16 x^{2}) + 3 (- 25)$

Factor $3$ out of $3 (16 x^{2}) + 3 (- 25)$ .

$3 (16 x^{2} - 25)$

Step 2

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$3 ({(4 x)}^{2} - 25)$

Step 3

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

$3 ({(4 x)}^{2} - 5^{2})$

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 $a = 4 x$ and $b = 5$ .

$3 ((4 x + 5) (4 x - 5))$

Remove unnecessary parentheses.

$3 (4 x + 5) (4 x - 5)$