# How do you multiply -2w( w-3)(w+1)?

Aug 15, 2015

$= \textcolor{b l u e}{- 2 {w}^{3} + 4 {w}^{2} + 6 w}$

#### Explanation:

$- \textcolor{b l u e}{2 w} \cdot \textcolor{g r e e n}{\left(w - 3\right)} \cdot \textcolor{red}{\left(w + 1\right)}$

First multiplying the terms within the first two brackets.
$- \textcolor{b l u e}{2 w} \cdot \textcolor{g r e e n}{\left(w - 3\right)}$

$= - \textcolor{b l u e}{\left(2 w\right)} \cdot \textcolor{g r e e n}{\left(w\right) - \textcolor{b l u e}{\left(2 w\right)} \cdot \left(- 3\right)}$

$= - 2 {w}^{2} + 6 w$ .
Now we multiply this expression with the term of the last bracket.

$= \left(- 2 {w}^{2} + 6 w\right) \cdot \textcolor{red}{\left(w + 1\right)}$

=color(blue)((-2w^2) * (w) -(2w^2) * 1) + color(red)((6w)*(w) +(6w)*1

$= - \textcolor{b l u e}{2 {w}^{3} - 2 {w}^{2}} + \textcolor{red}{6 {w}^{2} + 6 w}$

$= \textcolor{b l u e}{- 2 {w}^{3} + 4 {w}^{2} + 6 w}$