FOILing (and cleaner expansion methods)

Expand (a+b)(c+d). You get ac+ad+bc+bd. FOIL (Front Outer Inner Last) is a mnemonic for that. You multiply the FRONT ones first, a and c, then the OUTER ones, a and d, then the INNER ones, b and c, and last the LAST ones (oh coincidence), b and d.

The order you multiply in doesn't matter of course, it's just for easy memorization.

Here's why it comes out. (It took me years to get this :P)
(a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd.
Just some simple ol' distribution.

An expression with two terms is called a binomial. FOILing is one way to think of how to expand a product of binomials. It's not the only one.

You can do "multiply out all combinations", "distribute step by step", etc, etc.

Foiling only forks for two binomials. But the "multiply out all combinations" and "distribute step by step" expansion methods work for all products of expressions. Bottom line. They're better.

Tchea.