Question 881206
When you multiply factors with 2 or more terms, you end up making all the possible combinations of one term from one factor and another term from the other factor.
It is like picking shorts and shirts for an outfit.
(Black+Gray+Red) shorts, times (yellow+white+pink) shirts make
(B+G+R)(y+w+p)=By+Bw+Bp+Gy+Gw+Gp+Ry+Rw+Rp
 
You can only FOIL when each factor has 2 terms, because then you can make {{{2*2=4 different combinations that are easy to keep track of by calling them F, O, I, and L. It is acute acronym.
When you have 3 terms in one factor and 2 in the other, you can make {{{2*3=6}}} combinations so we need a 6-letter acronym, like FOIL@#.
No one has thought of cute names to call the products of the middle term of the 3-term factor (in this case {{{ab}}} ) times the first ( {{{a}}} ) and last ( {{{b}}} ) terms of a 2-term factor.
No one has thought of letter names for the 9 products formed when both factors have 3 terms.
Maybe it is lucky that we do not have to memorize more recipes to be applied without thinking or understanding.