What is the distributive property?

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a factor across the terms inside parentheses. The Distributive Property Calculator automates this process.

What expression formats are supported?

Expand mode accepts expressions like 3(x + 5), 2(a - b), or 4(2x + 7). Factor mode accepts polynomials with integer coefficients such as 6x + 9 or 4a - 8b.

Does it work with negative factors?

Yes. The Distributive Property Calculator handles negative factors, such as -2(a - b), correctly distributing the sign across all terms.

No. All calculations happen in your browser; nothing is sent to a server.

Distributive Property Calculator

How to Use Distributive Property Calculator

The Distributive Property Calculator gives you instant, step-by-step results for both expanding and factoring algebraic expressions.

Select a Mode — Choose Expand to apply the distributive property to a factored expression, or Factor to extract the greatest common factor from a polynomial.
Enter Your Expression — In Expand mode, type something like 3(x + 5) or 2(a - b). In Factor mode, type 6x + 9 or 4a - 8b. The Distributive Property Calculator parses your input automatically.
Read the Result — The Distributive Property Calculator displays the simplified expression along with a complete step-by-step breakdown so you can follow every multiplication or division.

This workflow makes the Distributive Property Calculator an ideal companion for algebra homework, classroom demonstrations, and quick mental-math checks.

Formula & Theory — Distributive Property Calculator

The Distributive Property Calculator implements the core distributive law of arithmetic and algebra:

a(b + c) = ab + ac        (expansion)
ab + ac  = a(b + c)       (factoring)

Symbol	Meaning
a	The outer factor (multiplier)
b, c	The terms inside parentheses
ab, ac	The distributed products

Expansion Direction

When you type 3(x + 5) into the Distributive Property Calculator, it multiplies 3 by each term:

3 × x = 3x
3 × 5 = 15
Result: 3x + 15

This is called distributing or expanding the expression. The Distributive Property Calculator shows each multiplication step individually so there is no ambiguity.

Factoring Direction

In Factor mode, the Distributive Property Calculator finds the Greatest Common Factor (GCF) of all terms. For 6x + 9, the GCF is 3, so:

6x ÷ 3 = 2x
9  ÷ 3 = 3
Result: 3(2x + 3)

Factoring with the Distributive Property Calculator is the reverse of expansion — useful for simplifying expressions before solving equations.

Use Cases for Distributive Property Calculator

The Distributive Property Calculator is valuable in a wide range of learning and practical scenarios:

Algebra homework — Students use the Distributive Property Calculator to check their manual expansions and make sure no sign errors crept in.
Mental math — The distributive property is a classic mental-math shortcut; e.g. 7 × 18 = 7(10 + 8) = 70 + 56 = 126. Verify these shortcuts with the Distributive Property Calculator.
Simplifying before solving — Expand 2(3x − 4) = 5x + 1 into 6x − 8 = 5x + 1 using the Distributive Property Calculator before isolating x.
Teaching aid — Teachers can project the Distributive Property Calculator in class to walk through examples step-by-step and highlight common mistakes.
Factoring for simplification — Before adding fractions or reducing rational expressions, factor each polynomial using the Distributive Property Calculator to identify common denominators quickly.

Whether you're a student, teacher, or just brushing up on algebra, the Distributive Property Calculator makes the distributive property easy to understand and apply.