Multiply Binomials Instantly

Expand with the
FOIL Method

Enter any binomial expression and get a beautiful, color-coded step-by-step solution using the First, Outer, Inner, Last method.

Enter expression

Type or paste two binomial expressions — e.g. (x + 3)(x - 5) or (2x - 1)²

Expanded Result

Visual Breakdown

First

Outer

Inner

Last

Step-by-Step Solution

Combine All Terms

Simplified Result

How It Works

Three Simple Steps

Master binomial multiplication in seconds with our intuitive calculator.

Enter Your Expression

Type any two binomials in the format (ax + b)(cx + d) or pick a quick example. Supports exponents, negatives, and decimals.

See the FOIL Breakdown

Watch each step — First, Outer, Inner, Last — calculated and color-coded so you can follow the method visually.

Get the Simplified Result

Like terms are combined automatically to give you the final expanded polynomial. Copy it to your clipboard in one click.

Features

Why Use Our Calculator?

Built for students, teachers, and anyone who works with algebra.

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Step-by-Step

See every multiplication step broken down with color-coded terms so you understand exactly how the FOIL method works.

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Instant Results

Get your expanded polynomial immediately. Supports variables, exponents, fractions, and complex binomial expressions.

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Visual Diagram

An interactive visual diagram shows which terms are being multiplied for each FOIL step with animated connections.

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Copy & Share

One-click copy lets you paste your result into homework, documents, or any other tool you're working with.

What is the FOIL Method?

The FOIL method is a technique for multiplying two binomials. FOIL is a mnemonic that stands for First, Outer, Inner, Last — representing the four multiplications you need to perform, then combine the results.

It's based on the distributive property of multiplication over addition. Given two binomials (a + b)(c + d), the FOIL method ensures you multiply every term in the first binomial by every term in the second.

FirstMultiply the first terms: a × c

OuterMultiply the outer terms: a × d

InnerMultiply the inner terms: b × c

LastMultiply the last terms: b × d

(a + b)(c + d) = ac + ad + bc + bd

The general FOIL expansion formula

After expanding, always combine like terms to simplify your final result. The FOIL method works with any pair of binomials containing variables, constants, or both.

FAQ

Frequently Asked Questions

Everything you need to know about the FOIL method and this calculator.

What is the FOIL method?

The FOIL method is a technique for multiplying two binomials. FOIL stands for First, Outer, Inner, Last — representing the four products you compute when expanding (a + b)(c + d) into ac + ad + bc + bd. After multiplying, you combine like terms to get the simplified result. It's essentially a mnemonic for applying the distributive property systematically.

How do I use this FOIL calculator?

Simply type or paste your binomial expression into the input field using the format (ax + b)(cx + d). You can also click any of the quick example buttons to try it instantly. Press the Calculate button or hit Enter to see the step-by-step FOIL expansion with color-coded terms and the simplified result. Use the Copy button to copy the answer to your clipboard.

Can FOIL be used for expressions with exponents?

Yes! This calculator supports variables with exponents. For example, you can expand (x² + 3)(x - 4) or (2x³ - 1)(x² + 5). The FOIL method works the same way — multiply each pair of terms and combine like terms. When multiplying terms with the same variable, add the exponents: x² × x³ = x⁵.

What does squaring a binomial mean?

Squaring a binomial means multiplying it by itself: (a + b)² = (a + b)(a + b). Using FOIL, this expands to a² + ab + ab + b² = a² + 2ab + b². You can enter expressions like (x - 7)² or (2x + 3)² directly into the calculator — it will automatically recognize the squared format and expand it correctly.

Is FOIL the same as the distributive property?

FOIL is a specific application of the distributive property for multiplying two binomials. The distributive property states that a(b + c) = ab + ac. When applied twice to (a + b)(c + d), you get all four FOIL products: ac + ad + bc + bd. FOIL is essentially a mnemonic shortcut to remember the order — First, Outer, Inner, Last — so you don't miss any terms.

Does FOIL work with more than two terms?

The FOIL method is specifically designed for multiplying two binomials (expressions with exactly two terms each). For trinomials or larger polynomials, you would use the full distributive property (also called the extended FOIL or grid/area method) where each term in the first polynomial is multiplied by every term in the second. Our calculator is optimized for binomial × binomial multiplication.

Expand with theFOIL Method