Factor n^2+16n+64

$n^{2} + 16 n + 64$

Rewrite $64$ as $8^{2}$ .

$n^{2} + 16 n + 8^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 n = 2 \cdot n \cdot 8$

Rewrite the polynomial.

$n^{2} + 2 \cdot n \cdot 8 + 8^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = n$ and $b = 8$ .

${(n + 8)}^{2}$