# How do you multiply (-4m^2-3n)^2?

Aug 21, 2017

See a solution process below:

#### Explanation:

We can use this rule to multiply this expression:

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

Substituting $\textcolor{red}{- 4 {m}^{2}}$ for color(red)(x) and substituting $\textcolor{b l u e}{- 3 n}$ for $\textcolor{b l u e}{y}$ gives:

${\left(\textcolor{red}{- 4 {m}^{2}} + \textcolor{b l u e}{- 3 n}\right)}^{2} \implies$

${\textcolor{red}{\left(- 4 {m}^{2}\right)}}^{2} + \left(2 \cdot \textcolor{red}{- 4 {m}^{2}} \cdot \textcolor{b l u e}{- 3 n}\right) + {\textcolor{b l u e}{\left(- 3 n\right)}}^{2} \implies$

$16 {m}^{4} + 24 {m}^{2} n + 9 {n}^{2}$