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

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

Step 1

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

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

Step 2

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

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

Step 3

Rewrite the polynomial.

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

Step 4

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

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