# Distributive Property Calculator

URL: https://speedycalculator.com/calculators/math/distributive-property/
Last updated: 2026-10-30

> The distributive property calculator expands a × (b + c + …) into a×b + a×c + … for up to four terms and confirms that both sides are equal.

## Inputs

- Factor outside the bracket (a)
- Terms inside the bracket
- Term 1
- Term 2
- Term 3
- Term 4

## Results

- a × (sum of terms)
- Sum of products a × term
- a × term 1
- a × term 2

## Formula

```
a × (b + c + d + e) = a×b + a×c + a×d + a×e
```

## Explanation

The distributive property links multiplication and addition. It is how we multiply mentally (7 × 104 = 7 × 100 + 7 × 4), how we expand brackets in algebra and how we factor expressions in reverse.

### How to use the Distributive Property Calculator

- **Factor outside the bracket (a)**
- **Terms inside the bracket**
- **Term 1**
- **Term 2**
- **Term 3**
- **Term 4**

Results update as you type, and everything is calculated in your browser.

### How it works

Each term inside the bracket is multiplied by the factor outside, and the products are added. The calculator evaluates both sides to show they agree.

### Inputs explained

FieldWhat to enterFactor outside the bracket (a)A numberTerms inside the bracketChoose one: 2, 3, 4Term 1A numberTerm 2A numberTerm 3A numberTerm 4A number

### What each result means

- **a × term 1** = [Factor outside the bracket (a)]×[Term 1]
- **a × term 2** = [Factor outside the bracket (a)]×[Term 2]

### Example values

How the main result changes when **Factor outside the bracket** changes and everything else stays at the example values above:

Factor outside the bracket (a)a × (sum of terms)3.53645.2554677288.7591010.51,092141,456

## Worked example

Inputs — Factor outside the bracket (a): 7; Terms inside the bracket: 2; Term 1: 100; Term 2: 4.

Results — **a × (sum of terms) = 728**; Sum of products a × term = 728; a × term 1 = 700; a × term 2 = 28.

## Key terms

- **Distributive property**: a(b + c) = ab + ac.

## FAQ

**What is the distributive property?**
a(b + c) = ab + ac – multiplication distributes over addition.

**Does it work with subtraction?**
Yes: a(b − c) = ab − ac.

**How does it help mental maths?**
Split awkward numbers: 6 × 98 = 6 × 100 − 6 × 2 = 588.

**Is factoring the reverse?**
Yes – ab + ac = a(b + c) takes out the common factor.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)