Distributive Property Calculator
Expand or factor expressions using the distributive property of multiplication over addition
Calculate Distributive Property
Use format: a(b+c+d) or (a+b+c)*d. Use * for multiplication.
Example formats:
3*(2+4+5) → expands to 3×2 + 3×4 + 3×5(7-2+3)*4 → expands to 7×4 - 2×4 + 3×4-2*(3+1-9) → expands to -2×3 + -2×1 + -2×(-9)Distributive Property Rules
Worked Examples
Example 1: Basic Expansion
Problem: 3(2 + 4 + 11)
Solution:
= 3 × 2 + 3 × 4 + 3 × 11
= 6 + 12 + 33
= 51
Example 2: With Negative Numbers
Problem: -2(3 + 1 - 9)
Solution:
= -2 × 3 + -2 × 1 + -2 × (-9)
= -6 - 2 + 18
= 10
Example 3: Factoring
Problem: 12 + 18 + 24
Solution:
Common factor: 6
= 6(2 + 3 + 4)
= 6(9) = 54
Properties Overview
Multiplication
a(b + c) = ab + ac
Distribute multiplication over addition
Division
(a + b) ÷ c = a/c + b/c
Distribute division over addition
Mixed Operations
a(b - c + d) = ab - ac + ad
Works with subtraction too
Quick Tips
The distributive property works both ways: expanding and factoring
Pay careful attention to positive and negative signs
Use parentheses to group terms clearly
Check your work by expanding factored forms
The property applies to variables as well as numbers
Understanding the Distributive Property
What is the Distributive Property?
The distributive property states that multiplying a number by a sum gives the same result as multiplying the number by each addend and then adding the products. In mathematical terms: a(b + c) = ab + ac.
Why is it Important?
- •Simplifies complex expressions
- •Essential for algebra and equation solving
- •Helps in mental math calculations
- •Foundation for polynomial operations
Common Applications
Expanding Expressions
3(x + 4) = 3x + 12
Factoring
6x + 9 = 3(2x + 3)
Mental Math
7 × 98 = 7(100 - 2) = 700 - 14 = 686
Extended Forms
Multiple Terms
a(b + c + d + e) = ab + ac + ad + ae
Both Sides
(a + b)(c + d) = ac + ad + bc + bd
With Subtraction
a(b - c) = ab - ac
Division Form
(a + b) ÷ c = a/c + b/c