Factor 125x^2-45

$125 x^{2} - 45$

Step 1

Factor $5$ out of $125 x^{2} - 45$ .

Factor $5$ out of $125 x^{2}$ .

$5 (25 x^{2}) - 45$

Factor $5$ out of $- 45$ .

$5 (25 x^{2}) + 5 (- 9)$

Factor $5$ out of $5 (25 x^{2}) + 5 (- 9)$ .

$5 (25 x^{2} - 9)$

Step 2

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$5 ({(5 x)}^{2} - 9)$

Step 3

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

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

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 $a = 5 x$ and $b = 3$ .

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

Remove unnecessary parentheses.

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