Given f(x) and g(x), find (f+g)(x),(f-g)(x),(f.g)(x), and (f/g)(x)

f(x)= 4x^2 -2x +8 , g(x)= 4-x^2

I'm having a bit of an issue with this one: I understand how to get all of the answers except for when I hit the (f.g)(x) part. They are saying the answer is: -4x^4 + 2x^3 + 8x^2 - 8x + 32. I keep getting the numbers all wrong. Can anyone explain in steps to me how to figure this out? Thanks!

f(x) = 4x^2 - 2x + 8 ; g(x) = 4 - x^2

(f.g)(x) = f(x).g(x)
= (4x^2 - 2x + 8)(4 - x^2)
= 4x^2(4 - x^2) - 2x(4 - x^2) + 8(4 - x^2)
= 16x^2 - 4x^4 - 8x + 2x^3 + 32 - 8x^2
= -4x^4 + 2x^3 + 16x^2 - 8x^2 - 8x + 32
= -4x^4 + 2x^3 + 8x^2 - 8x + 32

Just distribute the binomial on each term of the trinomial. That makes it much more easier.
And that's it. Hope I'm not too late.

For this problem you will need to do the "FOIL" Method.

(4x^2)(4)+(4x^2)(-x^2)+(-2x)(4)+(-2x)(…

After Foil you are left with

16x^2-4x^4-8x+2x^3+32-8x^2

Simplify and you get

-4x^4+2x^3+8x^2-8x+32

x=potato