Factor (x-4)(x^2-8x+16)

$(x - 4) (x^{2} - 8 x + 16)$

Step 1

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

$(x - 4) (x^{2} - 8 x + 4^{2})$

Step 2

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

$8 x = 2 \cdot x \cdot 4$

Step 3

Rewrite the polynomial.

$(x - 4) (x^{2} - 2 \cdot x \cdot 4 + 4^{2})$

Step 4

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

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