Question

How do you use FOIL to multiply `(x-2)^2 (x+17)`?

Answer 1

FOIL will only get you part of the way, but...

`(x-2)^2(x+17)`

`= (x^2-4x+4)(x+17)`

`= x^3+13x^2-64x+68`

Explanation:

FOIL will only get you part of the way since once you multiply two of the binomials together you will be left with multiplying a binomial by a trinomial - which is not covered by FOIL.

`(x-2)^2 = (x-2)(x-2)`

`= F + O + I + L` (First, Outside, Inside, Last)

`= (x*x)+(x*-2)+(-2*x)+(-2*-2)`

`=x^2-2x-2x+4`

`= x^2-4x+4`

Then using distributivity...

`(x^2-4x+4)(x+17)`

`=(x^2-4x+4)x + (x^2-4x+4)17`

`=x^3-4x^2+4x+17x^2-68x+68`

`=x^2+(17-4)x^2-(68-4)x+68`

`=x^2+13x^2-64x+68`