FOIL Method

In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product:

• First (“first” terms of each binomial are multiplied together)
• Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)
• Inner (“inside” terms are multiplied—second term of the first binomial and first term of the second)
• Last (“last” terms of each binomial are multiplied)

The general form is:

Note that is both a “first” term and an “outer” term; is both a “last” and “inner” term, and so forth. The order of the four terms in the sum is not important, and need not match the order of the letters in the word FOIL.

The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra, but many students and educators in the United States now use the word “foil” as a verb meaning “to expand the product of two binomials”. This neologism has not gained widespread acceptance in the mathematical community.