Factor 4n^2-16

$4 n^{2} - 16$

Step 1

Factor $4$ out of $4 n^{2} - 16$ .

Factor $4$ out of $4 n^{2}$ .

$4 (n^{2}) - 16$

Factor $4$ out of $- 16$ .

$4 n^{2} + 4 \cdot - 4$

Factor $4$ out of $4 n^{2} + 4 \cdot - 4$ .

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

Step 2

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

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

Step 3

Factor.

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

$4 ((n + 2) (n - 2))$

Remove unnecessary parentheses.

$4 (n + 2) (n - 2)$