FOIL Calculator
Multiply two binomials (ax+b)(cx+d) using the FOIL method with step-by-step breakdown.
About FOIL Calculator
FOIL stands for First, Outer, Inner, Last — the four products formed when multiplying two binomials (ax+b)(cx+d). The result is acx² + (ad+bc)x + bd.
Formula
FOIL Method
(ax+b)(cx+d) = acx² + (ad+bc)x + bd
- a
- First binomial x-coeff
- b
- First binomial constant
- c
- Second binomial x-coeff
- d
- Second binomial constant
Worked example
With the default values below, FOIL Calculator returns Product of 2x² - 5x - 12. Change any input above and every figure here is recalculated in your browser.
Inputs used
- a (first binomial, x coeff)
- 2
- b (first binomial, constant)
- 3
- c (second binomial, x coeff)
- 1
- d (second binomial, constant)
- -4
Results
- Product
- 2x² - 5x - 12
- First (a·c)x²
- 2.0000
- Outer (a·d)x
- -8.0000
- Inner (b·c)x
- 3.0000
- Last (b·d)
- -12.0000
Step by step
- 1Values used
- 2FOIL Method
- 3Product= 2x² - 5x - 12
- 4First (a·c)x²= 2.0000
- 5Outer (a·d)x= -8.0000
- 6Inner (b·c)x= 3.0000
- 7Last (b·d)= -12.0000
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What does FOIL stand for?
First (multiply the first terms), Outer (multiply the outer terms), Inner (multiply the inner terms), Last (multiply the last terms).
Does FOIL work for trinomials?
No — FOIL is specifically for two binomials. For larger polynomials, use the distributive property or the polynomial expansion calculator.