FOIL is a memory aid for multiplying two binomials: multiply the First terms, the Outer terms, the Inner terms and the Last terms, then combine the two middle products. It is a special case of the distributive property.
How to use the FOIL Calculator
- Mode
- a
- b
- c
- d
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The four products are listed separately, then the Outer and Inner products – both x-terms – are combined. In reverse mode the calculator factors ax² + bx + c instead.
Formula
(ax + b)(cx + d) = acx² + (ad + bc)x + bd
Worked example
Inputs — Mode: Multiply (ax + b)(cx + d); a: 2; b: 3; c: 1; d: -4.
Results — Result = 2x² − 5x − 12; FOIL steps = First: 2x · x = 2x²
Outer: 2x · (−4) = −8x
Inner: 3 · x = 3x
Last: 3 · (−4) = −12
Combine like terms: 2x² − 5x − 12; x² coefficient = 2; x coefficient = −5; Constant = −12.
Key terms
- Binomial
- A polynomial with two terms.
- Distributive property
- a(b + c) = ab + ac.
Frequently asked questions
What does FOIL stand for?
First, Outer, Inner, Last – the four products when multiplying two binomials.
Does FOIL work for trinomials?
No. For longer polynomials, multiply every term by every term (the distributive property).
What is (x + 3)(x − 3)?
x² − 9, a difference of squares: the outer and inner terms cancel.
What is reverse FOIL?
Factoring: finding the binomials that multiply to a given trinomial.