# How do you multiply -3(2x + 5) • (x² - 3x + 2)?

May 16, 2017

$= - 6 {x}^{3} + 3 {x}^{2} + 33 x - 30$

#### Explanation:

You are multiplying $3$ factors together.

Multiplication is commutative and the associative law also applies here, so you can really multiply them in any order that you like.

I have chosen to multiply the two brackets together first and then multiply that product by $- 3$ at the end.

$- 3 \times \left(2 x + 5\right) \times \left({x}^{2} - 3 x + 2\right)$

$= - 3 \times \left[\textcolor{b l u e}{\left(2 x + 5\right) \times \left({x}^{2} - 3 x + 2\right)}\right]$

$= - 3 \times \left[\textcolor{b l u e}{2 {x}^{3} - 6 {x}^{2} + 4 x + 5 {x}^{2} - 15 x + 10}\right] \text{ } \leftarrow$ simplify

$= - 3 \left(2 {x}^{3} - {x}^{2} - 11 x + 10\right)$

$= - 6 {x}^{3} + 3 {x}^{2} + 33 x - 30$