Factor by Grouping x^2+4xy+4y^2

$x^{2} + 4 x y + 4 y^{2}$

Step 1

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

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

Step 2

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

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

Step 3

Rewrite the polynomial.

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

Step 4

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

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