Factor x^2+2xy+y^2

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

Step 1

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

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

Step 2

Rewrite the polynomial.

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

Step 3

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

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