Factor ab-a^3b^3

$a b - a^{3} b^{3}$

Factor $a b$ out of $a b - a^{3} b^{3}$ .

Factor $a b$ out of $a b$ .

$a b (1) - a^{3} b^{3}$

Factor $a b$ out of $- a^{3} b^{3}$ .

$a b (1) + a b (- a^{2} b^{2})$

Factor $a b$ out of $a b (1) + a b (- a^{2} b^{2})$ .

$a b (1 - a^{2} b^{2})$

Rewrite $1$ as $1^{2}$ .

$a b (1^{2} - a^{2} b^{2})$

Rewrite $a^{2} b^{2}$ as ${(a b)}^{2}$ .

$a b (1^{2} - {(a b)}^{2})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = a b$ .

$a b ((1 + a b) (1 - (a b)))$

Factor.

Remove parentheses.

$a b ((1 + a b) (1 - a b))$

Remove unnecessary parentheses.

$a b (1 + a b) (1 - a b)$