FOIL Calculator
Multiply two binomials (ax+b)(cx+d) using the FOIL method with step-by-step algebraic solutions. Get expanded form and coefficients instantly free online.
About This Calculator
The FOIL calculator expands the product of two binomials using the First, Outer, Inner, Last method. Given two binomials (ax + b)(cx + d), the calculator computes the expanded quadratic expression acx^2 + (ad + bc)x + bd and shows each multiplication step separately.
FOIL is a specific case of the distributive property used in algebra to multiply two-term expressions. This calculator handles positive and negative integer, fractional, and decimal coefficients. Students can verify homework, teachers can demonstrate the method, and anyone learning algebra can follow the step-by-step breakdown to understand how binomial multiplication works.
How FOIL works: First -- multiply the first terms a and c. Outer -- multiply the outer terms a and d. Inner -- multiply the inner terms b and c. Last -- multiply the last terms b and d. The results are then combined into a simplified quadratic expression.
Frequently Asked Questions
What does FOIL stand for?
FOIL stands for First, Outer, Inner, Last -- the four multiplication steps when expanding two binomials (ax+b)(cx+d). Multiply the First terms (axc), Outer terms (axd), Inner terms (bxc), and Last terms (bxd), then combine like terms.
Can the FOIL method be used with more than two terms?
No, FOIL specifically applies to multiplying two binomials (two-term expressions). For polynomials with three or more terms, use the distributive property or the multiplying polynomials calculator.
What happens when coefficients are negative?
Negative coefficients are handled the same way -- just apply the sign during multiplication. For example, (2x - 3)(-x + 5) gives First: -2x^2, Outer: 10x, Inner: 3x, Last: -15, combining to -2x^2 + 13x - 15.
Is the FOIL calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration or hidden charges.
What if the result shows a zero coefficient?
If a coefficient is zero after combining like terms, that term is omitted from the expanded form. For example, (x+2)(x-2) = x^2 - 4 -- the x term disappears because 2x + (-2x) = 0.
Can I share my FOIL calculation results?
Yes, use the Share button to copy the URL with your inputs. Anyone opening that link will see the same expression and results automatically.