# How do you multiply (4a+b)^2?

Sep 5, 2016

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

#### Explanation:

We can express ${\left(4 a + b\right)}^{2}$ as $\left(4 a + b\right) \left(4 a + b\right)$

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.

This may be done as follows.

$\left(\textcolor{red}{4 a + b}\right) \left(4 a + b\right) = \textcolor{red}{4 a} \left(4 a + b\right) \textcolor{red}{+ b} \left(4 a + b\right)$

distribute the brackets.

$\Rightarrow 16 {a}^{2} + 4 a b + 4 a b + {b}^{2}$

collecting like terms gives $16 {a}^{2} + 8 a b + {b}^{2}$

$\Rightarrow {\left(4 a + b\right)}^{2} = 16 {a}^{2} + 8 a b + {b}^{2}$