How do you simplify (u + 7v ) ^ { 2} ?

Jun 26, 2017

${u}^{2} + 14 u v + 49 {v}^{2}$

Explanation:

$\left(\textcolor{b l u e}{u} \textcolor{\mathrm{da} r k red}{+ 7 v}\right) \left(\textcolor{red}{u} \textcolor{g r e e n}{+ 7 v}\right)$

You proceed to FOIL it:

Where you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\left(\textcolor{b l u e}{u}\right) \left(\textcolor{red}{u}\right) = {u}^{2}$

$\left(\textcolor{b l u e}{u}\right) \left(\textcolor{g r e e n}{7 v}\right) = 7 u v$

Now you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\textcolor{\mathrm{da} r k red}{\left(7 v\right)} \left(\textcolor{red}{u}\right) = 7 u v$

$\textcolor{\mathrm{da} r k red}{\left(7 v\right)} \left(\textcolor{g r e e n}{7 v}\right) = 49 {v}^{2}$

Now combine them:

${u}^{2} + 7 u v + 7 u v + 49 {v}^{2}$

Simplify:

${u}^{2} + 14 u v + 49 {v}^{2}$