The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra.

[3] Many students and educators in the US now use the word "FOIL" as a verb meaning "to expand the product of two binomials".

The FOIL rule converts a product of two binomials into a sum of four (or fewer, if like terms are then combined) monomials.

A visual memory tool can replace the FOIL mnemonic for a pair of polynomials with any number of terms.

The table equivalent to the FOIL rule looks like this: In the case that these are polynomials, (ax + b)(cx + d), the terms of a given degree are found by adding along the antidiagonals: so

For instance: Alternate methods based on distributing forgo the use of the FOIL rule, but may be easier to remember and apply.