Multiplying Binomials Calculator

Multiply two binomials and see the expanded polynomial with the FOIL method laid out step by step.

Last updated: March 2026 | By ForgeCalc Engineering

FOIL Solver

Binomial expansion

First x Coefficient

First Constant

Second x Coefficient

Second Constant

FOIL Steps

1.First: (1x) × (1x) = 1x²

2.Outer: (1x) × (3) = 3x

3.Inner: (2) × (1x) = 2x

4.Last: (2) × (3) = 6

5.Combine like terms: 1x² + (3 + 2)x + 6 = x² + 5x + 6

Expanded Form

x² + 5x + 6

x²

const

What Is the FOIL Method?

FOIL is a shortcut for multiplying two binomials by combining the First, Outer, Inner, and Last terms. The result is usually a trinomial.

How to Multiply Binomials with FOIL

Multiply the first terms.
Multiply the outer terms.
Multiply the inner terms.
Multiply the last terms and combine like terms.

(ax + b)(cx + d) = acx² + (ad + bc)x + bd

Worked Example

Example: (x + 2)(x + 3) = x² + 5x + 6.

x² + 3x + 2x + 6 = x² + 5x + 6

Frequently Asked Questions

Can I use FOIL for larger polynomials?

FOIL is designed for binomials. For larger expressions, use the distributive property more broadly.

What if a coefficient is negative?

Negative coefficients are handled normally and affect the sign of the resulting terms.

Does the result always have three terms?

Usually yes, but like terms may combine or cancel, changing the final number of terms.

Can coefficients be decimals?

Yes. Any finite real coefficients are accepted.

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