# FOIL Calculator

Multiply two binomials using the FOIL method with step-by-step work. See First, Outer, Inner, Last terms and the simplified polynomial. Free FOIL calculator.

## What this calculates

Multiply two binomials using the FOIL method and see every step. Enter the coefficients and constants for (ax + b)(cx + d) and get the expanded and simplified result.

## Inputs

- **First binomial: a (coefficient of x)** — The coefficient of x in (ax + b). For just 'x', enter 1.
- **First binomial: b (constant)** — The constant term in (ax + b).
- **Second binomial: c (coefficient of x)** — The coefficient of x in (cx + d). For just 'x', enter 1.
- **Second binomial: d (constant)** — The constant term in (cx + d).

## Outputs

- **First (a*c)x²** — formatted as text — First terms multiplied: a * c * x².
- **Outer (a*d)x** — formatted as text — Outer terms multiplied: a * d * x.
- **Inner (b*c)x** — formatted as text — Inner terms multiplied: b * c * x.
- **Last (b*d)** — formatted as text — Last terms multiplied: b * d.
- **Expanded Form** — formatted as text — All four FOIL terms written out.
- **Simplified Result** — formatted as text — The final simplified polynomial after combining like terms.

## Details

FOIL is a mnemonic for multiplying two binomials: **F**irst, **O**uter, **I**nner, **L**ast. It ensures you multiply every term in the first binomial by every term in the second.

**FOIL Steps for (ax + b)(cx + d):**

1. **First:** Multiply the first terms: a * c = ac (gives the x² term)
2. **Outer:** Multiply the outer terms: a * d = ad (gives an x term)
3. **Inner:** Multiply the inner terms: b * c = bc (gives an x term)
4. **Last:** Multiply the last terms: b * d = bd (gives the constant)

**Result:** acx² + (ad + bc)x + bd

**Example:**

(2x + 3)(x - 5) = 2x² + (-10x) + 3x + (-15) = 2x² - 7x - 15

**Beyond FOIL:**

FOIL only works for two binomials. For multiplying a binomial by a trinomial or larger expressions, use the distributive property (every term by every term). FOIL is just a special case of distribution that is easy to remember for the most common case in algebra.

## Frequently Asked Questions

**Q: What does FOIL stand for?**

A: FOIL stands for First, Outer, Inner, Last. It describes the four multiplications needed when multiplying two binomials: (a + b)(c + d). First means a*c, Outer means a*d, Inner means b*c, and Last means b*d. After computing all four products, you combine like terms for the final answer.

**Q: Can I use FOIL for more than two binomials?**

A: No. FOIL only works for multiplying exactly two binomials. If you need to multiply three or more expressions, FOIL the first two, then multiply the result by the third using the distributive property. For example, (x+1)(x+2)(x+3): first FOIL (x+1)(x+2) = x² + 3x + 2, then distribute (x² + 3x + 2)(x+3).

**Q: How is FOIL related to the distributive property?**

A: FOIL is just a specific application of the distributive property. When you distribute (a + b)(c + d), you multiply every term in the first factor by every term in the second: ac + ad + bc + bd. FOIL gives these same four products a memorable order. The distributive property works for any number of terms, while FOIL is limited to two binomials.

**Q: What is a common mistake with FOIL?**

A: The most common mistake is forgetting to combine the Outer and Inner terms. After computing all four products, the two middle terms (Outer and Inner) are both x terms and must be added together. Another common error is sign mistakes when one or both constants are negative.

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Source: https://vastcalc.com/calculators/math/foil
Category: Math
Last updated: 2026-04-08