Factor a^2-16a+64

$a^{2} - 16 a + 64$

Step 1

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

$a^{2} - 16 a + 8^{2}$

Step 2

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

$16 a = 2 \cdot a \cdot 8$

Step 3

Rewrite the polynomial.

$a^{2} - 2 \cdot a \cdot 8 + 8^{2}$

Step 4

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

${(a - 8)}^{2}$