# How do you simplify (2x^2 -5x+8) * (x-3)?

Jun 23, 2018

See a 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.

$\left(\textcolor{red}{2 {x}^{2}} - \textcolor{red}{5 x} + \textcolor{red}{8}\right) \left(\textcolor{b l u e}{x} - \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{2 {x}^{2}} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{2 {x}^{2}} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{3}\right) + \left(\textcolor{red}{8} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{8} \times \textcolor{b l u e}{3}\right)$

$2 {x}^{3} - 6 {x}^{2} - 5 {x}^{2} + 15 x + 8 x - 24$

We can now combine like terms:

$2 {x}^{3} + \left(- 6 - 5\right) {x}^{2} + \left(15 + 8\right) x - 24$

$2 {x}^{3} + \left(- 11\right) {x}^{2} + 23 x - 24$

$2 {x}^{3} - 11 {x}^{2} + 23 x - 24$