Factor 2c^2-32d^2

$2 c^{2} - 32 d^{2}$

Step 1

Factor $2$ out of $2 c^{2} - 32 d^{2}$ .

Factor $2$ out of $2 c^{2}$ .

$2 (c^{2}) - 32 d^{2}$

Factor $2$ out of $- 32 d^{2}$ .

$2 (c^{2}) + 2 (- 16 d^{2})$

Factor $2$ out of $2 (c^{2}) + 2 (- 16 d^{2})$ .

$2 (c^{2} - 16 d^{2})$

Step 2

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

$2 (c^{2} - {(4 d)}^{2})$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 4 d$ .

$2 ((c + 4 d) (c - (4 d)))$

Step 4

Factor.

Multiply $4$ by $- 1$ .

$2 ((c + 4 d) (c - 4 d))$

Remove unnecessary parentheses.

$2 (c + 4 d) (c - 4 d)$