Find the Product (2a+b)^2

${(2 a + b)}^{2}$

Rewrite ${(2 a + b)}^{2}$ as $(2 a + b) (2 a + b)$ .

$(2 a + b) (2 a + b)$

Expand $(2 a + b) (2 a + b)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a + b) + b (2 a + b)$

Apply the distributive property.

$2 a (2 a) + 2 a b + b (2 a + b)$

Apply the distributive property.

$2 a (2 a) + 2 a b + b (2 a) + b \cdot b$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a b + b (2 a) + b \cdot b$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a b + b (2 a) + b \cdot b$

Multiply $a$ by $a$ .

$2 \cdot 2 a^{2} + 2 a b + b (2 a) + b \cdot b$

Multiply $2$ by $2$ .

$4 a^{2} + 2 a b + b (2 a) + b \cdot b$

Rewrite using the commutative property of multiplication.

$4 a^{2} + 2 a b + 2 b a + b \cdot b$

Multiply $b$ by $b$ .

$4 a^{2} + 2 a b + 2 b a + b^{2}$

Add $2 a b$ and $2 b a$ .

Move $b$ .

$4 a^{2} + 2 a b + 2 a b + b^{2}$

Add $2 a b$ and $2 a b$ .

$4 a^{2} + 4 a b + b^{2}$