I'd like to take an EPEE to FOIL. Or maybe a SABER.

Multiply everything inside the second set of parentheses by what's outside the parentheses, which in the case of two binomials is the first binomial. And then do it again with the other set of parentheses. This method will work with trinomials as well without leaving you scratching your head.

I've had students who could multiply a trinomial by a binomial because they didn't know what to do with the extra term because they'd learned a short-cut but not the concept.

Interestingly, when I try to demonstrate using integers instead of variables, the point gets lost because they finally start using the Order of Operations, correctly, and add what's inside the parentheses first. Sigh.