Evaluate (x+2y)^2

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

Rewrite ${(x + 2 y)}^{2}$ as $(x + 2 y) (x + 2 y)$ .

$(x + 2 y) (x + 2 y)$

Expand $(x + 2 y) (x + 2 y)$ using the FOIL Method.

Apply the distributive property.

$x (x + 2 y) + 2 y (x + 2 y)$

Apply the distributive property.

$x \cdot x + x (2 y) + 2 y (x + 2 y)$

Apply the distributive property.

$x \cdot x + x (2 y) + 2 y x + 2 y (2 y)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $2$ by $2$ .

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

Add $2 x y$ and $2 y x$ .

Move $y$ .

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

Add $2 x y$ and $2 x y$ .

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