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

Jun 13, 2017

#### Answer:

Use the distributive property.

The multiplied form is $6 {n}^{4} - 9 {n}^{3} - 12 {n}^{2}$

#### Explanation:

The distributive property tells us that:

$\textcolor{red}{a} \cdot \left(b + c\right)$

$\textcolor{red}{a} \cdot b + \textcolor{red}{a} \cdot c$

So we can use this property to distribute the $- 3 {n}^{2}$ term:

$\textcolor{red}{- 3 {n}^{2}} \left(- 2 {n}^{2} + 3 n + 4\right)$

$= \textcolor{red}{- 3 {n}^{2}} \cdot \left(- 2 {n}^{2}\right) + \textcolor{red}{- 3 {n}^{2}} \cdot \left(3 n\right) + \textcolor{red}{- 3 {n}^{2}} \cdot 4$

Now just multiply each group of terms together. Remember that two negatives make a positive.

$= 6 {n}^{4} - 9 {n}^{3} - 12 {n}^{2}$

Final Answer