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
| Field | What to enter |
|---|---|
| Factor outside the bracket (a) | A number |
| Terms inside the bracket | Choose one: 2, 3, 4 |
| Term 1 | A number |
| Term 2 | A number |
| Term 3 | A number |
| Term 4 | A 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) |
|---|---|
| 3.5 | 364 |
| 5.25 | 546 |
| 7 | 728 |
| 8.75 | 910 |
| 10.5 | 1,092 |
| 14 | 1,456 |
Formula
a × (b + c + d + e) = a×b + a×c + a×d + a×e
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.
Frequently asked questions
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.