# How do you simplify (-8p+5)(-5p^2+4p-7)?

Aug 19, 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.

$\left(\textcolor{red}{- 8 p} + \textcolor{red}{5}\right) \left(\textcolor{b l u e}{- 5 {p}^{2}} + \textcolor{b l u e}{4 p} - \textcolor{b l u e}{7}\right)$ becomes:

$\left(\textcolor{red}{8 p} \times \textcolor{b l u e}{5 {p}^{2}}\right) - \left(\textcolor{red}{8 p} \times \textcolor{b l u e}{4 p}\right) + \left(\textcolor{red}{8 p} \times \textcolor{b l u e}{7}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{5 {p}^{2}}\right) + \left(\textcolor{red}{5} \times \textcolor{b l u e}{4 p}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{7}\right)$

$40 {p}^{3} - 32 {p}^{2} + 56 p - 25 {p}^{2} + 20 p - 35$

We can now group and combine like terms:

$40 {p}^{3} - 32 {p}^{2} - 25 {p}^{2} + 56 p + 20 p - 35$

$40 {p}^{3} + \left(- 32 - 25\right) {p}^{2} + \left(56 + 20\right) p - 35$

$40 {p}^{3} + \left(- 57\right) {p}^{2} + 76 p - 35$

$40 {p}^{3} - 57 {p}^{2} + 76 p - 35$