What is the process of expanding quadratic equation

Question

I am currently doing a math problem: $(a-b)(a^2+ab+b^2)$
However, I am not sure how I can actually expand this problem

1. Do I multiply $(a-b)$ with each individual item within the other bracket?

Answer 1

I find it easier to expand the term with fewer subterms first. So I would write $(a-b)(a^2+ab+b^2)=a(a^2+ab+b^2)-b(a^2+ab+b^2)$ Now distribute the $a$ and $b$ over the terms in the parentheses, giving a total of six terms. You should find a great deal of cancellation.

Answer 2

The general rule is that for expanding $(\star\star)(\dagger\dagger)$, you multiply every monomial within the left-hand parentheses times every monomial within the right-hand parentheses. In your case, you’ll get six products, ’cause there are two monomials between the left-hand parentheses, and three between the right-hand ones. You’ll find when you do the calculation that you get a lot of cancellations, but that’s a special property of this particular product.

If I may be cranky and inveigh for a moment, it looks to me as if you were taught the dreaded FOIL incantation. This is surely one of the most damaging pedagogical errors ever inflicted on students.