Multiply two binomials step by step using the FOIL method. Enter your first binomial (e.g. 2x + 3) and second binomial (e.g. x - 5), and get back the expanded result broken down into First, Outer, Inner, and Last term products — plus the fully simplified polynomial.
x² Coefficient
--
x Coefficient
--
Constant Term
--
F — First Terms Product
--
O — Outer Terms Product
--
I — Inner Terms Product
--
L — Last Terms Product
--
The FOIL method is a technique for multiplying two binomials in algebra. It stands for First, Outer, Inner, and Last — describing which pairs of terms you multiply together. After multiplying all four pairs, you combine like terms to get the simplified result.
FOIL is an acronym: F = First (multiply the first terms of each binomial), O = Outer (multiply the outermost terms), I = Inner (multiply the innermost terms), L = Last (multiply the last terms of each binomial). All four products are then added together.
For two binomials (ax + b) and (cx + d), FOIL gives: (ax + b)(cx + d) = ac·x² + ad·x + bc·x + bd, which simplifies to ac·x² + (ad + bc)·x + bd. The x² coefficient comes from the First terms, the x coefficient from the Outer and Inner terms combined, and the constant from the Last terms.
Yes — the FOIL method is specifically designed for multiplying two binomials. Each binomial has exactly two terms (e.g. 2x + 1 and 5x + 7), and FOIL systematically multiplies all four pairings to expand the expression.
The distributive property states that a(b + c) = ab + ac. FOIL is simply a mnemonic for applying the distributive property twice when multiplying two binomials. It ensures every term in the first binomial is multiplied by every term in the second binomial — no term gets missed.
They are inverse operations. FOIL expands a product of two binomials into a polynomial. Reverse FOIL (also called factoring by grouping or factoring trinomials) works backwards — starting from a trinomial like x² + 5x + 6 and finding the two binomials (x + 2)(x + 3) that produce it.
Absolutely. When a coefficient or constant is negative, you simply carry the negative sign through the multiplication. For example, (2x − 3)(x + 4) treats the second term as −3, so the Inner product is −3·x = −3x and the Last product is −3·4 = −12. Enter negative values in the constant fields to handle this.
FOIL strictly applies to the product of exactly two binomials (two terms each). If you have a trinomial (three terms) or higher polynomial, you need to use the full distributive property or other polynomial multiplication techniques instead of FOIL.