Find the Product (2x+y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ .

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

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

Move $y$ .

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

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

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