Factor x^2+16x+64

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

Step 1

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

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

Step 2

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

$16 x = 2 \cdot x \cdot 8$

Step 3

Rewrite the polynomial.

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

Step 4

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

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