Factor 16n^2-1

$16 n^{2} - 1$

Step 1

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

${(4 n)}^{2} - 1$

Step 2

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

${(4 n)}^{2} - 1^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 n$ and $b = 1$ .

$(4 n + 1) (4 n - 1)$