SOLUTION: We have this homework question on a worksheet. Our algebra teacher said we need to be sure on the answer because we will have it on at least one quiz. Here is what he gave us.

You can put this solution on YOUR website!
Because you're multiplying a binomial by a trinomial (2 terms by 3 terms) your answer before simplifying will have 6 terms. I sometimes find it easier when working on paper to write all 6 terms on two lines, the first line being and the second line being lining up all of my terms (x^2, x^3, etc...) like:
1st line:
2nd line.....:
Now you should recognize that you when you add the two lines you'll combine x^2 and x terms to get:

Which is what you got, so you'll probably be fine.