Distributive Property Formula
The Formula
When to use: Three packs of (2 red + 4 blue) = (3 \times 2 red) + (3 \times 4 blue) = 6 red + 12 blue.
Quick Example
Notation
What This Formula Means
Multiplication distributes over addition: a(b + c) = ab + ac, linking two operations together.
Three packs of (2 red + 4 blue) = (3 \times 2 red) + (3 \times 4 blue) = 6 red + 12 blue.
Formal View
Worked Examples
Example 1
easySolution
- 1 Identify the two terms inside the parentheses: x and 7.
- 2 Distribute 4 to each term inside the parentheses: 4 \cdot x + 4 \cdot 7.
- 3 Simplify: 4x + 28.
Answer
Example 2
mediumCommon Mistakes
- Only distributing to the first term inside the parentheses: 3(x + 4) = 3x + 4 instead of 3x + 12
- Forgetting to distribute the sign: -(a + b) = -a + b instead of -a - b
- Trying to distribute multiplication over multiplication: a(bc) \neq (ab)(ac)
Why This Formula Matters
Foundation of algebra; enables factoring and expanding expressions.
Frequently Asked Questions
What is the Distributive Property formula?
Multiplication distributes over addition: a(b + c) = ab + ac, linking two operations together.
How do you use the Distributive Property formula?
Three packs of (2 red + 4 blue) = (3 \times 2 red) + (3 \times 4 blue) = 6 red + 12 blue.
What do the symbols mean in the Distributive Property formula?
a(b + c) is shorthand for a \times (b + c); the factor distributes to each term inside
Why is the Distributive Property formula important in Math?
Foundation of algebra; enables factoring and expanding expressions.
What do students get wrong about Distributive Property?
Works forwards (distributing) and backwards (factoring): ab + ac = a(b+c) is equally valid.
What should I learn before the Distributive Property formula?
Before studying the Distributive Property formula, you should understand: multiplication, addition.
Want the Full Guide?
This formula is covered in depth in our complete guide:
Commutative, Associative, and Distributive Properties →