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: See more

The method is most commonly used to multiply linear binomials. For example,
If either binomial involves See more

The FOIL method is equivalent to a two-step process involving the distributive law:
$${\displaystyle {\begin{aligned}(a+b)(c+d)&=a(c+d)+b(c+d)\\&=ac+ad+bc+bd.\end{aligned}}}$$
In the first step, the (c + d) is distributed over the addition in first … See more

The FOIL rule converts a product of two binomials into a sum of four (or fewer, if like terms are then combined) monomials. The reverse process is called factoring or factorization. In particular, if the proof above is read in reverse it illustrates the technique called See more

A visual memory tool can replace the FOIL mnemonic for a pair of polynomials with any number of terms. Make a table with the terms of the first polynomial on the left edge and the terms of the second on the top edge, then fill in the table with products of multiplication. … See more

The FOIL rule cannot be directly applied to expanding products with more than two multiplicands or multiplicands with more than two summands. However, applying the associative law and recursive foiling allows one to expand such products. For instance: See more

• Binomial theorem
• Factorization See more