Factor 2a^2b-32a^4b

$2 a^{2} b - 32 a^{4} b$

Factor $2 a^{2} b$ out of $2 a^{2} b - 32 a^{4} b$ .

Factor $2 a^{2} b$ out of $2 a^{2} b$ .

$2 a^{2} b (1) - 32 a^{4} b$

Factor $2 a^{2} b$ out of $- 32 a^{4} b$ .

$2 a^{2} b (1) + 2 a^{2} b (- 16 a^{2})$

Factor $2 a^{2} b$ out of $2 a^{2} b (1) + 2 a^{2} b (- 16 a^{2})$ .

$2 a^{2} b (1 - 16 a^{2})$

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

$2 a^{2} b (1^{2} - 16 a^{2})$

Rewrite $16 a^{2}$ as ${(4 a)}^{2}$ .

$2 a^{2} b (1^{2} - {(4 a)}^{2})$

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 $b = 4 a$ .

$2 a^{2} b ((1 + 4 a) (1 - (4 a)))$

Factor.

Multiply $4$ by $- 1$ .

$2 a^{2} b ((1 + 4 a) (1 - 4 a))$

Remove unnecessary parentheses.

$2 a^{2} b (1 + 4 a) (1 - 4 a)$