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

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

Step 1

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

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

Step 2

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

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

Step 3

Rewrite the polynomial.

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

Step 4

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

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