Question

How do you multiply `(a + 2)(a^2 - 5a +9)`?

Answer 1

You can use distributivity to find:

`(a+2)(a^2-5a+9) = a^3-3a^2-a+18`

Explanation:

`(a+2)(a^2-5a+9)`

`=a(a^2-5a+9)+2(a^2-5a+9)`

`=(a^3-5a^2+9a)+(2a^2-10a+18)`

`=a^3-5a^2+2a^2+9a-10a+18`

`=a^3+(-5+2)a^2+(9-10)a+18`

`=a^3-3a^2-a+18`

Alternatively, look at each power of `a` in descending order and collect the terms that multiply to contribute to the coefficient of that power of `a`:

`a^3` : `a*a^2 = a^3`

`a^2` : `(a*-5a)+(2*a^2) = -5a^2 + 2a^2 = -3a^2`

`a` : `(a*9) + (2*-5a) = 9a-10a = -a`

`1` : `2 * 9 = 18`