Factor 5x^3-125x

$5 x^{3} - 125 x$

Step 1

Factor $5 x$ out of $5 x^{3} - 125 x$ .

Factor $5 x$ out of $5 x^{3}$ .

$5 x (x^{2}) - 125 x$

Factor $5 x$ out of $- 125 x$ .

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

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

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

Step 2

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

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

Step 3

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

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

Remove unnecessary parentheses.

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