Factor 3x^5-27x^3

$3 x^{5} - 27 x^{3}$

Step 1

Factor $3 x^{3}$ out of $3 x^{5} - 27 x^{3}$ .

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

$3 x^{3} (x^{2}) - 27 x^{3}$

Factor $3 x^{3}$ out of $- 27 x^{3}$ .

$3 x^{3} (x^{2}) + 3 x^{3} (- 9)$

Factor $3 x^{3}$ out of $3 x^{3} (x^{2}) + 3 x^{3} (- 9)$ .

$3 x^{3} (x^{2} - 9)$

Step 2

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

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

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 $b = 3$ .

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

Remove unnecessary parentheses.

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