Distributive Property
Multiplication distributes over addition: a(b + c) = ab + ac.
About this topic
The distributive property says that multiplying a sum by a number is the same as multiplying each part and adding: a(b + c) = ab + ac. So 4(x + 3) = 4x + 12. It works for subtraction too, and a negative factor changes every sign inside.
This property lets you expand brackets, do mental maths (7 × 98 = 7 × 100 − 7 × 2) and later factor expressions by running it in reverse. Area models of rectangles split into two parts show why it is true. A rectangle of height 4 and width x + 3 has the same area as two rectangles, 4 by x and 4 by 3.
For a negative factor, −2(3x − 5) = −6x + 10, since −2 times −5 is positive. When there are two brackets, each term in the first multiplies each in the second, which is the basis of the FOIL method: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. Shopping gives a natural example: 3 shirts at 12 dollars and 3 hats at 8 dollars cost 3(12 + 8) = 60 dollars either way.
A frequent mistake is multiplying only the first term, so 3(x + 4) becomes 3x + 4. Another is forgetting that a minus in front of brackets flips every sign inside. Factoring, which undoes distribution, is central to solving quadratics later.
Key ideas
- Multiply the outside term by every inside term
- Watch signs with negatives
- It is used in expanding and factoring
Quick check
Use cases: where Distributive Property helps
- Homework: review the key idea behind Distributive Property before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Distributive Property without notes.
- Visual learning: play with the interactive lab to see how Distributive Property changes when you adjust its inputs.
- Teaching a friend: explain Distributive Property in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Distributive Property?
Multiplication distributes over addition: a(b + c) = ab + ac.
What will I learn in Distributive Property?
Multiply the outside term by every inside term. Watch signs with negatives. It is used in expanding and factoring.
Is Distributive Property part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Distributive Property lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Distributive Property?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.