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FOIL Calculator

Expand (ax + b)(cx + d) using First, Outer, Inner, Last

(ax+b)(cx+d)

FOIL Formula

(ax+b)(cx+d)=acx²+(ad+bc)x+bd

The FOIL formula expands two binomials by multiplying every term in the first binomial by every term in the second. The first product creates the x² term, the outer and inner products combine into the x term, and the last product becomes the constant term. After these four products are found, like terms are combined to produce a simplified quadratic expression.

⚠Note: This calculator expands two linear binomials. For larger polynomial products, use a polynomial multiplication tool.

What Is FOIL?

FOIL is a memory method for multiplying two binomials. It organizes the four products so that the result can be simplified into a quadratic expression.

First

Multiply ax and cx to get acx².

Outer

Multiply ax and d to get adx.

Inner

Multiply b and cx to get bcx.

Last

Multiply b and d to get the constant term bd.

💡 Example: (2x+3)(4x-5)=8x²+2x-15.

Applications

Binomial ProductsQuadraticsFactoring Checks

Frequently Asked Questions

What is a FOIL calculator?▼

A FOIL calculator expands two binomials such as (ax+b)(cx+d) into a quadratic expression.

What does FOIL stand for?▼

FOIL stands for First, Outer, Inner, Last.

What is the formula for (ax+b)(cx+d)?▼

The expanded form is acx²+(ad+bc)x+bd.

Can FOIL handle negative terms?▼

Yes. Negative coefficients follow normal sign rules during multiplication and addition.

When is FOIL used?▼

FOIL is used in algebra homework, factoring checks, quadratic expansion, and simplifying expressions.

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