# How do you multiply (6a + b)^2?

Apr 6, 2018

${36}^{2} + 12 a b + {b}^{2}$

#### Explanation:

${\left(6 a + b\right)}^{2}$ is the same as saying $\left(6 a + b\right) \left(6 a + b\right)$.

We will use the mnemonic $\text{FOIL}$ to solve this equation. $\text{FOIL}$ stand for:
$\textcolor{b l u e}{\text{F}}$irsts
$\textcolor{p u r p \le}{\text{O}}$uters
$\textcolor{b r o w n}{\text{I}}$nners
$\textcolor{g r e e n}{\text{L}}$asts

$\left(6 a + b\right) \left(6 a + b\right)$

Firsts: $6 a \times 6 a \rightarrow {\textcolor{b l u e}{\text{36a}}}^{\textcolor{b l u e}{2}}$

Outers: $6 a \times b \rightarrow \textcolor{p u r p \le}{\text{6ab}}$

Inners: $b \times 6 a \rightarrow \textcolor{b r o w n}{\text{6ab}}$

Lasts: $b \times b \rightarrow {\textcolor{g r e e n}{b}}^{\textcolor{g r e e n}{2}}$

Now put them all together and simplify:

${36}^{2} + 6 a b + 6 a b + {b}^{2}$

${36}^{2} + 12 a b + {b}^{2}$