Factor 32v^2-8

$32 v^{2} - 8$

Step 1

Factor $8$ out of $32 v^{2} - 8$ .

Factor $8$ out of $32 v^{2}$ .

$8 (4 v^{2}) - 8$

Factor $8$ out of $- 8$ .

$8 (4 v^{2}) + 8 (- 1)$

Factor $8$ out of $8 (4 v^{2}) + 8 (- 1)$ .

$8 (4 v^{2} - 1)$

Step 2

Rewrite $4 v^{2}$ as ${(2 v)}^{2}$ .

$8 ({(2 v)}^{2} - 1)$

Step 3

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

$8 ({(2 v)}^{2} - 1^{2})$

Step 4

Factor.

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

$8 ((2 v + 1) (2 v - 1))$

Remove unnecessary parentheses.

$8 (2 v + 1) (2 v - 1)$