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Distributive Law Calculator

Online distributive property checker. Enter a, b, c to verify a×(b+c)=a×b+a×c with full derivation—great for elementary arithmetic.

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a × (b + c) = a×b + a×c
a×ba×cabc
Factor outside
First inside
Second inside

📖 Tutorial | Distributive Property

1. Definition
Multiplying a sum by a number gives the same as multiplying each addend and adding the products.
2. Formula & Notation
aOutside factor
b, cAddends inside
3. Properties & Laws
  • a(b+c)=ab+ac;
  • For subtraction a(b−c)=ab−ac;
  • Reversible (factoring);
  • Works for integers, decimals, fractions.
4. Steps
  1. Enter a, b, c;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 3(4+5).
Solution: left 27; right 12+15=27.
6. Common Pitfalls
a multiplies both b and c;
Do not skip a term;
Associative is multiplication only.

❓ FAQ | Distributive Property

Distributive property?
a(b+c)=ab+ac.
3(4+5)?
27.
Vs. associative?
Distributive has addition; associative only multiplication.
Subtraction?
a(b−c)=ab−ac.
Reverse use?
Factoring, e.g. 3·7+3·3=30.
Use?
Mental math and algebra.