Factor 50n^2-8

$50 n^{2} - 8$

Step 1

Factor $2$ out of $50 n^{2} - 8$ .

Factor $2$ out of $50 n^{2}$ .

$2 (25 n^{2}) - 8$

Factor $2$ out of $- 8$ .

$2 (25 n^{2}) + 2 (- 4)$

Factor $2$ out of $2 (25 n^{2}) + 2 (- 4)$ .

$2 (25 n^{2} - 4)$

Step 2

Rewrite $25 n^{2}$ as ${(5 n)}^{2}$ .

$2 ({(5 n)}^{2} - 4)$

Step 3

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

$2 ({(5 n)}^{2} - 2^{2})$

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 $a = 5 n$ and $b = 2$ .

$2 ((5 n + 2) (5 n - 2))$

Remove unnecessary parentheses.

$2 (5 n + 2) (5 n - 2)$