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

May 21, 2017

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.

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

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

$2 {x}^{3} + 10 {x}^{2} - 6 x - 3 {x}^{2} - 15 x + 9$

We can now group and combine like terms:

$2 {x}^{3} + 10 {x}^{2} - 3 {x}^{2} - 6 x - 15 x + 9$

$2 {x}^{3} + \left(10 - 3\right) {x}^{2} + \left(- 6 - 15\right) x + 9$

$2 {x}^{3} + 7 {x}^{2} + \left(- 21\right) x + 9$

$2 {x}^{3} + 7 {x}^{2} - 21 x + 9$