Factor x^3-25x

$x^{3} - 25 x$

Step 1

Factor $x$ out of $x^{3} - 25 x$ .

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

$x \cdot x^{2} - 25 x$

Factor $x$ out of $- 25 x$ .

$x \cdot x^{2} + x \cdot - 25$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 25$ .

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

Step 2

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

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

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 $b = 5$ .

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

Remove unnecessary parentheses.

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