Factor z^2+16z+64

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

Step 1

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

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

Step 2

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

$16 z = 2 \cdot z \cdot 8$

Step 3

Rewrite the polynomial.

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

Step 4

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

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