Factor x^2-8xy+16y^2

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

Step 1

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

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

Step 2

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

$8 x y = 2 \cdot x \cdot (4 y)$

Step 3

Rewrite the polynomial.

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

Step 4

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

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