# How do you simplify (2x + 5)(3x^3 - 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.

$\left(\textcolor{red}{2 x} + \textcolor{red}{5}\right) \left(\textcolor{b l u e}{3 {x}^{3}} - \textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{x}\right)$ becomes:

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

$6 {x}^{4} - 2 {x}^{3} + 2 {x}^{2} + 15 {x}^{3} - 5 {x}^{2} + 5 x$

We can now group and combine like terms:

$6 {x}^{4} - 2 {x}^{3} + 15 {x}^{3} + 2 {x}^{2} - 5 {x}^{2} + 5 x$

$6 {x}^{4} + \left(- 2 + 15\right) {x}^{3} + \left(2 - 5\right) {x}^{2} + 5 x$

$6 {x}^{4} + 13 {x}^{3} - 3 {x}^{2} + 5 x$