# How do you simplify 2/3np^2(30p^2+9n^2p-12)?

May 27, 2017

$20 n {p}^{4} + 6 {n}^{3} {p}^{3} - 8 n {p}^{2}$

#### Explanation:

The first step is distributing the $\textcolor{red}{\frac{2}{3}} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{2}}$ across the parentheses.

$\left(\textcolor{red}{\frac{2}{3}} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{2}}\right) \left(\textcolor{red}{30} \textcolor{b l u e}{{p}^{2}}\right) + \left(\textcolor{red}{\frac{2}{3}} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{2}}\right) \left(\textcolor{red}{9} \textcolor{g r e e n}{{n}^{2}} \textcolor{b l u e}{p}\right) - \left(\textcolor{red}{\frac{2}{3}} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{2}}\right) \left(\textcolor{red}{12}\right)$

The colored variables/constants were added to differentiate variables from constants and to show clearly what is being multiplied.

Now we need to individually multiply these terms.

$\textcolor{red}{20} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{4}} + \textcolor{red}{6} \textcolor{g r e e n}{{n}^{3}} \textcolor{b l u e}{{p}^{3}} - \textcolor{red}{8} \textcolor{g r e e n}{n} \textcolor{b l u e}{{p}^{2}}$

And that's all there is to it.