<span> FOIL is a mnemonic rule for multiplying binomial (that is, two-term) algebraic expressions. </span> <span>FOIL abbreviates the sequence "First, Outside, Inside, Last"; it's a way of remembering that the product is the sum of the products of those four combinations of terms. </span>
<span>For instance, if we multiply the two expressions </span> <span>(x + 1) (x + 2) </span> <span>then the result is the sum of these four products: </span> <span>x times x (the First terms of each expression) </span> <span>x times 2 (the Outside pair of terms) </span> <span>1 times x (the Inside pair of terms) </span> <span>1 times 2 (the Last terms of each expression) </span> <span>and so </span> <span>(x + 1) (x + 2) = x^2 + 2x + 1x + 2 = x^2 + 3x + 2 </span> <span>[where the ^ is the usual way we indicate exponents here in Answers, because they're hard to represent in an online text environment]. </span>
<span>The reason the two processes resemble each other is that multiplication is multiplication; the difference in the ways we represent the factors doesn't make it a fundamentally different operation. </span>