Factor 18r^2-32

$18 r^{2} - 32$

Step 1

Factor $2$ out of $18 r^{2} - 32$ .

Factor $2$ out of $18 r^{2}$ .

$2 (9 r^{2}) - 32$

Factor $2$ out of $- 32$ .

$2 (9 r^{2}) + 2 (- 16)$

Factor $2$ out of $2 (9 r^{2}) + 2 (- 16)$ .

$2 (9 r^{2} - 16)$

Step 2

Rewrite $9 r^{2}$ as ${(3 r)}^{2}$ .

$2 ({(3 r)}^{2} - 16)$

Step 3

Rewrite $16$ as $4^{2}$ .

$2 ({(3 r)}^{2} - 4^{2})$

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 $a = 3 r$ and $b = 4$ .

$2 ((3 r + 4) (3 r - 4))$

Remove unnecessary parentheses.

$2 (3 r + 4) (3 r - 4)$