Distributive Property
Multiplication spreads over addition.
Key idea
Multiplication spreads over addition.
In depth
a(b + c) = ab + ac. Multiplying a sum is the same as multiplying each part and adding. It is the area of a rectangle split into two smaller rectangles, and the basis for expanding and factoring.
Worked example
3(x + 4) = 3x + 12. And −2(x − 5) = −2x + 10.
Formula
Real-world uses
- Mental maths such as 7 × 98 = 7 × 100 − 7 × 2
- Expanding area formulas for rectangles with extra strips
Common mistake
Multiplying only the first term, or dropping the sign change when distributing a negative.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Distributive Property?
Multiplication spreads over addition. It is a topic at the beginner level in Algebra.
What is the formula for Distributive Property?
The key formula is a(b + c) = ab + ac.
Where is Distributive Property used in real life?
Real-world examples: Mental maths such as 7 × 98 = 7 × 100 − 7 × 2; Expanding area formulas for rectangles with extra strips.
What should I learn before Distributive Property?
Make sure you are comfortable with Like Terms, the previous topic in Algebra.
What is a common mistake with Distributive Property?
Multiplying only the first term, or dropping the sign change when distributing a negative.
How can I practise Distributive Property?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Distributive Property?
Move on to Simplifying Expressions next.
Related beginner topics in Algebra
- Variables and Expressions – Letters stand for unknown or changing numbers in expressions.
- Evaluating Expressions – Substitute values for variables and simplify.
- Like Terms – Terms with the same variable part can be combined.
- Simplifying Expressions – Combine like terms and apply distribution to write expressions compactly.
- Writing Expressions from Words – Translate phrases like “three more than twice a number” into algebra.
- One-Step Equations – Undo one operation to isolate the variable.