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

Feb 13, 2017

See the entire simplification process below:

#### Explanation:

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

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

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

$3 {x}^{5} + 3 {x}^{4} - 2 {x}^{4} - 2 {x}^{3} - 2 {x}^{2} - 2 x$

We can now combine like terms:

$3 {x}^{5} + \left(3 - 2\right) {x}^{4} - 2 {x}^{3} - 2 {x}^{2} - 2 x$

$3 {x}^{5} + 1 {x}^{4} - 2 {x}^{3} - 2 {x}^{2} - 2 x$

$3 {x}^{5} + {x}^{4} - 2 {x}^{3} - 2 {x}^{2} - 2 x$

Or, if required, we can factor out an $x$ term:

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