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

Jun 9, 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.

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

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

$5 {x}^{4} - 25 {x}^{2} + 10 x - 3 {x}^{3} + 15 x - 6$

We can now group and combine like terms:

$5 {x}^{4} - 3 {x}^{3} - 25 {x}^{2} + 10 x + 15 x - 6$

$5 {x}^{4} - 3 {x}^{3} - 25 {x}^{2} + \left(10 + 15\right) x - 6$

$5 {x}^{4} - 3 {x}^{3} - 25 {x}^{2} + 25 x - 6$