FOIL Calculator

FOIL is a mnemonic for multiplying two binomials: First, Outer, Inner, Last. It ensures you multiply every term in the first binomial by every term in the second.

FOIL Steps for (ax + b)(cx + d)

1. First: Multiply the first terms: a * c = ac (gives the x² term)
2. Outer: Multiply the outer terms: a * d = ad (gives an x term)
3. Inner: Multiply the inner terms: b * c = bc (gives an x term)
4. Last: Multiply the last terms: b * d = bd (gives the constant)

Result: acx² + (ad + bc)x + bd

Example

(2x + 3)(x - 5) = 2x² + (-10x) + 3x + (-15) = 2x² - 7x - 15

Beyond FOIL

FOIL only works for two binomials. For multiplying a binomial by a trinomial or larger expressions, use the distributive property (every term by every term). FOIL is just a special case of distribution that is easy to remember for the most common case in algebra.