Question

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

Answer 1

`-s^5+5s^3+7s^2-35`

Explanation:

The general method of distributing two binomials is:

`(color(red)a+color(blue)b)(color(green)c+color(purple)d)=color(red)acolor(green)c+color(red)acolor(purple)d+color(blue)bcolor(green)c+color(blue)bcolor(purple)d`

So here, distributing everything, we get:

`(-s^2+5)(s^3-7)=(-s^2)(s^3)+(-s^2)(-7)+5(s^3)+5(-7)`

`=-s^5+5s^3+7s^2-35`