Calculadora FOIL (produto de binômios)

Expande (ax + b)(cx + d) = ac·x² + (ad+bc)·x + bd pelo método FOIL.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

Coef. de x²
10,00
Coef. de x
29,00
Termo const.
21,00

Formula

(ax+b)(cx+d) = ac·x² + (ad+bc)·x + bd

About this calculator

The FOIL Calculator expands the product of two linear binomials of the form (ax + b)(cx + d) using the FOIL method. FOIL stands for First, Outer, Inner, Last, which are the four necessary multiplications: First (a·c·x²), Outer (a·d·x), Inner (b·c·x), and Last (b·d). The result is a quadratic trinomial: ac·x² + (ad+bc)·x + bd. This tool automates the process, avoiding manual errors.

It is useful for algebra students checking homework answers, teachers preparing examples, or anyone dealing with algebraic expressions. For instance, expanding (2x + 3)(4x - 5) yields 8x² + 2x - 15. Usage is simple: enter coefficients a, b, c, and d, and the result appears instantly.

Cautions: ensure binomials are in the form (ax + b)(cx + d). Include negative signs in coefficients (e.g., for (2x - 3), use b = -3). The calculator handles integers, decimals, and fractions. It does not apply to binomials with exponents other than 1 or more than two terms.

Frequently asked questions

What does FOIL stand for?

FOIL stands for First, Outer, Inner, Last, indicating the order of multiplications: first terms, outer, inner, and last.

Can I use the calculator for binomials like (x + 2)(x - 3)?

Yes. Enter a=1, b=2, c=1, d=-3. The result is x² - x - 6.

Does the calculator work with fractions?

Yes, it accepts fractional coefficients. For example, (1/2 x + 2)(3x - 1) yields 1.5x² + 5.5x - 2.

What if the binomial has more than two terms?

The calculator only expands two linear binomials. For larger polynomials, use a polynomial multiplication calculator.

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