What is a math FOIL?

In math, FOIL is an acronym that reminds people how to expand the multiplication of two expressions in parentheses. FOIL stands for First, Outside, Inside, and Last, which is the order in which one should multiply the terms in the parentheses.

As an example, one can use FOIL to expand the expression (3x + 2)(4x + 6). Multiplying the first terms from each set of parentheses gives 12x^2. Multiplying the outside terms gives 18x. The product of the inside terms is 8x, and the product of the last two terms is 12. The final expanded equation using FOIL is (3x + 2)(4x + 6) = 12x^2 + 26x + 18.