"Foiling" IS distributing.
The FOIL method is used to multiply binomials, or to multiply (x + 3) by (3x -12) for example.
But FOILing can ONLY be used with binomials. Let find out why:
FOILing means first multiplying the FIRST terms together, or x and 3x to get 3x2
Then multiply the OUTSIDE terms together, or x and -12 to get -12x.
Then multiply the INSIDE terms together, or 3 and 3x to get 9x.
The multiply the LAST terms together, or 3 and -12 to get -36.
Simplify by adding like terms to get 3x2 -3x -36.
If we were to use distribution to multiply (x + 3) by (3x -12) we'd multiply x by 3x.
Then multiply x by -12.
Then multiply 3 by 3x.
Then multiply 3 by -12.
So FOILing IS distributing, but one cannot use the FOIL method on anything else but binomials.
i.e. we can't use the FOIL method to find the product of a trinomial and an binomial.