# How do you simplify (x - 9)(x - 2)(3x + 2)?

Jun 7, 2017

See a solution process below:

#### Explanation:

First, multiply the two terms on the right. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(x - 9\right) \left(\textcolor{red}{x} - \textcolor{red}{2}\right) \left(\textcolor{b l u e}{3 x} + \textcolor{b l u e}{2}\right)$ becomes:

$\left(x - 9\right) \left(\left(\textcolor{red}{x} \times \textcolor{b l u e}{3 x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{3 x}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{2}\right)\right)$

$\left(x - 9\right) \left(3 {x}^{2} + 2 x - 6 x - 4\right)$

We can now combine like terms:

$\left(x - 9\right) \left(3 {x}^{2} + \left(2 - 6\right) x - 4\right)$

$\left(x - 9\right) \left(3 {x}^{2} + \left(- 4\right) x - 4\right)$

$\left(x - 9\right) \left(3 {x}^{2} - 4 x - 4\right)$

Now, do the same thing for the two remaining terms:

$\left(\textcolor{red}{x} - \textcolor{red}{9}\right) \left(\textcolor{b l u e}{3 {x}^{2}} - \textcolor{b l u e}{4 x} - \textcolor{b l u e}{4}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{3 {x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{4 x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{4}\right) - \left(\textcolor{red}{9} \times \textcolor{b l u e}{3 {x}^{2}}\right) + \left(\textcolor{red}{9} \times \textcolor{b l u e}{4 x}\right) + \left(\textcolor{red}{9} \times \textcolor{b l u e}{4}\right)$

$3 {x}^{3} - 4 {x}^{2} - 4 x - 27 {x}^{2} + 36 x + 36$

We can now group and combine like terms:

$3 {x}^{3} - 4 {x}^{2} - 27 {x}^{2} - 4 x + 36 x + 36$

$3 {x}^{3} + \left(- 4 - 27\right) {x}^{2} + \left(- 4 + 36\right) x + 36$

$3 {x}^{3} + \left(- 31\right) {x}^{2} + 32 x + 36$

$3 {x}^{3} - 31 {x}^{2} + 32 x + 36$