Distributive Property Calculator
Expand expressions using the distributive property a(b + c) = ab + ac with step-by-step solutions.
Try These Examples
Understanding the Distributive Property
The Rule: a(b + c) = ab + ac
When you multiply a number or variable by a sum inside parentheses, you multiply it by each term inside and then add the results.
Example 1:
3(x + 4)
= 3·x + 3·4
= 3x + 12
Example 2:
-2(x - 5)
= -2·x + (-2)·(-5)
= -2x + 10
Common Mistakes to Avoid
- ✗Forgetting to distribute to ALL terms: 2(x + 3) ≠ 2x + 3
- ✗Sign errors with negatives: -3(x - 2) = -3x + 6, not -3x - 6
- ✓Always multiply the outside by EVERY term inside
The Reverse: Factoring Out
You can also use distributive property in reverse to factor:
6x + 12 = 6(x + 2)
Find the GCF and factor it out of each term.
About Distributive Property Calculator - Expand & Simplify
Apply the distributive property to expand and simplify algebraic expressions. Step-by-step solutions for distribution problems.
Our **Distributive Property Calculator** expands expressions by distributing multiplication over addition/subtraction. Enter expressions like a(b + c) and get ab + ac with step-by-step explanations. For multiplying polynomials, use our Multiplying Polynomials Calculator.
The distributive property states that a(b + c) = ab + ac. This fundamental property is used constantly in algebra for expanding, simplifying, and solving equations. Our calculator applies it systematically.
Master distribution—the foundation of polynomial manipulation, equation solving, and algebraic simplification. See exactly how each term is distributed with our educational step-by-step format.
Key Features
Why Use This Tool?
Common Use Cases
Algebra: Expand expressions for simplification.
Equation Solving: Clear parentheses in equations.
Factoring: Verify by distributing factors.
Mental Math: Break complex multiplications.
Related Tools
How to Use
Enter the multiplier
Enter the expression to distribute over
Click Distribute
View expanded result and steps