Factor c^2-8c+16

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

Step 1

Rewrite $16$ as $4^{2}$ .

$c^{2} - 8 c + 4^{2}$

Step 2

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

$8 c = 2 \cdot c \cdot 4$

Step 3

Rewrite the polynomial.

$c^{2} - 2 \cdot c \cdot 4 + 4^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = c$ and $b = 4$ .

${(c - 4)}^{2}$