FOIL Calculator — Binomial Multiplication Step by Step
Enter the four coefficients of two linear binomials (ax + b)(cx + d) and see the FOIL expansion worked out step by step — First, Outside, Inside, Last — with the simplified polynomial result.
F (First × First): x × x
O (Outer × Last): x × -2
I (Inner × First): 3 × x
L (Last × Last): 3 × -2
Combine like terms (x terms)
Final expanded form
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(ax + b)(cx + d) = ac·x² + (ad+bc)·x + bd. F = ac·x², O = ad·x, I = bc·x, L = bd. Combine the Outside and Inside terms (they are both x terms) and you get the standard trinomial form. Works for any real coefficients, including negatives.
Формула
How this is calculated
FOIL is a mnemonic for multiplying two binomials (expressions with two terms each). Each letter tells you which pair of terms to multiply:
• **F**irst — multiply the first terms of each binomial: ax · cx = ac·x² • **O**utside — multiply the outermost terms: ax · d = ad·x • **I**nside — multiply the innermost terms: b · cx = bc·x • **L**ast — multiply the last terms: b · d = bd
After computing all four products, combine the two middle terms (ad + bc)·x because they are like terms (both have exactly one x). The result is the trinomial ac·x² + (ad + bc)·x + bd.
FOIL is really just the distributive property applied twice — every term in the first binomial multiplies every term in the second binomial — so it extends to larger polynomials too (though the FOIL name only applies to two binomials). Coefficients can be any real numbers, including negative values and decimals.
Поширені запитання
FOIL applies specifically to two binomials (two terms each). For trinomials or larger polynomials you use the general distributive property — multiply every term of the first polynomial by every term of the second — which generates more product pairs. FOIL is a shortcut that happens to list all four products for the 2×2 case.
Negative coefficients follow normal multiplication rules: a negative times a positive gives a negative, and a negative times a negative gives a positive. Enter negative values directly (e.g. b = −3 means the binomial is ax − 3). The calculator handles the signs automatically.
If a = 0, the first factor collapses to just a constant (0·x + b = b), and the product simplifies to b(cx + d) — no x² term. The calculator treats this as a degenerate binomial and still expands it using the distributive property, showing 0 for the x² coefficient.
Також відомий як
TG we-Calculate Editorial Team. (2026). FOIL Calculator — Binomial Multiplication Step by Step [Online calculator]. TG we-Calculate. https://we-calculate.com/uk/calculator/foil-calculator
TG we-Calculate Editorial Team. "FOIL Calculator — Binomial Multiplication Step by Step." TG we-Calculate. 2026. https://we-calculate.com/uk/calculator/foil-calculator.
TG we-Calculate Editorial Team, "FOIL Calculator — Binomial Multiplication Step by Step," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/uk/calculator/foil-calculator
@misc{wecalculate_foil_calculator, title = {FOIL Calculator — Binomial Multiplication Step by Step}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/uk/calculator/foil-calculator}}, year = {2026}, note = {TG we-Calculate} }
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