# How do you multiply (2x-5)(x^2+6x-4)?

Mar 19, 2017

See the entire solution 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.

$\left(\textcolor{red}{2 x} - \textcolor{red}{5}\right) \left(\textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{6 x} - \textcolor{b l u e}{4}\right)$ becomes:

$\left(\textcolor{red}{2 x} \times \textcolor{b l u e}{{x}^{2}}\right) + \left(\textcolor{red}{2 x} \times \textcolor{b l u e}{6 x}\right) - \left(\textcolor{red}{2 x} \times \textcolor{b l u e}{4}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{6 x}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{4}\right)$

$2 {x}^{3} + 12 {x}^{2} - 8 x - 5 {x}^{2} - 30 x + 20$

We can now group and combine like terms:

$2 {x}^{3} + 12 {x}^{2} - 5 {x}^{2} - 8 x - 30 x + 20$

$2 {x}^{3} + \left(12 - 5\right) {x}^{2} + \left(- 8 - 30\right) x + 20$

$2 {x}^{3} + 7 {x}^{2} - 38 x + 20$