Factor by Grouping x^2-2xy+y^2

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

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

$2 x y = 2 \cdot x \cdot y$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot y + y^{2}$

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

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