Factor 5x^3-45x

$5 x^{3} - 45 x$

Step 1

Factor $5 x$ out of $5 x^{3} - 45 x$ .

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

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

Factor $5 x$ out of $- 45 x$ .

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

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

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

Step 2

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

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

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 $b = 3$ .

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

Remove unnecessary parentheses.

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