Factor 3x^3-75x

$3 x^{3} - 75 x$

Step 1

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

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

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

Factor $3 x$ out of $- 75 x$ .

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

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

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

Step 2

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

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

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 $b = 5$ .

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

Remove unnecessary parentheses.

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