# How do you multiply (-13u+v^2)^2?

Mar 8, 2018

${v}^{4} - 26 u {v}^{2} + 169 {u}^{2}$

#### Explanation:

${\left({v}^{2} - 13 u\right)}^{2}$
${\left({v}^{2}\right)}^{2} - 2 \left({v}^{2}\right) \left(13 u\right) + {\left(13 u\right)}^{2}$
${v}^{4} - 26 u {v}^{2} + 169 {u}^{2}$

Mar 8, 2018

The formula for ${\left(a + b\right)}^{2}$ is ${a}^{2} + 2 a b + {b}^{2}$. Let's apply this to our problem.

#### Explanation:

${\left(- 13 u + {v}^{2}\right)}^{2}$ = ${\left(- 13 u\right)}^{2} + 2 \left(- 13 u\right) \left({v}^{2}\right) + {\left({v}^{2}\right)}^{2}$

$- 13 u \cdot - 13 u = 169 {u}^{2}$
$2 \left(- 13 u\right) \left({v}^{2}\right) = - 26 u {v}^{2}$
${v}^{2} \cdot {v}^{2} = {v}^{4}$

Therefore, our answer is $169 {u}^{2} - 26 u {v}^{2} + {v}^{4}$.

Mar 8, 2018

$169 {u}^{2} - 26 u {v}^{2} + {v}^{4}$

#### Explanation:

In general
$\textcolor{w h i t e}{\text{XXX}} {\left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{red}{a}}^{2} + 2 \textcolor{red}{a} \textcolor{b l u e}{b} + {\textcolor{b l u e}{b}}^{2}$

So
color(white)("XXX")(color(red)(-13u)+color(blue)v^2))^2

$\textcolor{w h i t e}{\text{XXXXXXXX}} = {\left(\textcolor{red}{- 13 u}\right)}^{2} + 2 \cdot \left(\textcolor{red}{- 13 u}\right) \cdot \textcolor{b l u e}{{v}^{2}} + {\left(\textcolor{b l u e}{{v}^{2}}\right)}^{2}$

$\textcolor{w h i t e}{\text{XXXXXXXX}} = 169 {u}^{2} - 26 u {v}^{2} + {v}^{4}$