# How do you multiply (-s^2+5)(s^3-7)?

Apr 4, 2017

$- {s}^{5} + 5 {s}^{3} + 7 {s}^{2} - 35$

#### Explanation:

The general method of distributing two binomials is:

$\left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) \left(\textcolor{g r e e n}{c} + \textcolor{p u r p \le}{d}\right) = \textcolor{red}{a} \textcolor{g r e e n}{c} + \textcolor{red}{a} \textcolor{p u r p \le}{d} + \textcolor{b l u e}{b} \textcolor{g r e e n}{c} + \textcolor{b l u e}{b} \textcolor{p u r p \le}{d}$

So here, distributing everything, we get:

$\left(- {s}^{2} + 5\right) \left({s}^{3} - 7\right) = \left(- {s}^{2}\right) \left({s}^{3}\right) + \left(- {s}^{2}\right) \left(- 7\right) + 5 \left({s}^{3}\right) + 5 \left(- 7\right)$

$= - {s}^{5} + 5 {s}^{3} + 7 {s}^{2} - 35$