FOIL (which stands for First, Outer, Inner, Last) is a memory trick
that is limited to multiplying two binomials:
(a + b)(c + d) = ac + ad + bc + bd.
There is nothing wrong with reciting "first, outer, inner, last", as
far as it goes, but it does not extend to larger problems. For
(a + b)(c + d + e) = ___.
If you rely on FOIL as a memory trick you're stuck. If, however, you
remember that each term in the first group gets multiplied by each
term in the second group, this is just about as easy as before:
(a + b)(c + d + e) = ac + ad + ae + bc + bd + be.
Just put your left finger on "a" and cycle through the three terms on
the right. Then put your left finger on "b" and cycle through them
again. Now try this:
(a + b + c)(d + e + f) = ___.
Follow the same principle.
I tell my students about the FOIL method, because some already know
it, but I then show them the general pattern (an extension of the
distributive law), which I recommend as better in the long run.