# How do you find the product (a+4b)^2?

Apr 16, 2017

${a}^{2} + 8 a b + 16 {b}^{2}$

#### Explanation:

${\left(a + 4 b\right)}^{2} = \left(a + 4 b\right) \left(a + 4 b\right)$

Use the exponent rule $x \cdot x = {x}^{1} {x}^{1} = {x}^{1 + 1} = {x}^{2}$

Use the commutative property of multiplication: $a \cdot b = b \cdot a$

Use distribution to multiply:

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

$= {a}^{2} + 4 a b + 4 a b + 16 {b}^{2}$

$= {a}^{2} + 8 a b + 16 {b}^{2}$