Find the Product (a+2b)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $2$ by $2$ .

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

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

Move $b$ .

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

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

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