Learn distributive property
The distributive property multiplies the factor outside parentheses by every term inside. It rewrites a product as an equivalent sum or difference.
You will multiply an outside factor by every term inside parentheses.
The idea in plain English
Distributing means sharing the outside number with every term inside the parentheses.
If two terms are inside, the outside factor must be multiplied twice.
How to recognise this kind of question
- A number or variable sits directly beside parentheses.
- The parentheses contain two or more terms.
- The instruction says expand, distribute, or simplify.
Quick decision: Draw one arrow from the outside factor to every term inside.
The method
- Multiply the outside factor by the variable term.
- Multiply the same factor by the constant term.
- Keep each sign and simplify the products.
Worked examples
3(2x + 4)
- 3 × 2x = 6x.
- 3 × 4 = 12.
Answer: 6x + 12
−2(3x − 5)
- Multiply −2 × 3x = −6x.
- Multiply −2 × −5 = +10.
Answer: −6x + 10
Your turn—with help
4(x + 6)
Need a hint?
The 4 must multiply both x and 6.
Show the answer and steps
- 4 × x = 4x.
- 4 × 6 = 24.
- Combine the products: 4x + 24.
Answer: 4x + 24
Watch out for this mistake
Incorrect: 3(2x + 4) = 6x + 4
Why it fails: The 3 was multiplied by the first term but not the second.
Do this instead: Multiply both terms: 6x + 12.
Quick check
Try these without looking. Then open each answer to check your thinking.
3(y + 2)
Need a hint?
Multiply 3 twice.
Show the answer and steps
- 3 × y = 3y.
- 3 × 2 = 6.
Answer: 3y + 6
5(2a − 1)
Need a hint?
Keep the minus sign with 1.
Show the answer and steps
- 5 × 2a = 10a.
- 5 × −1 = −5.
Answer: 10a − 5
−3(m + 4)
Need a hint?
A negative times a positive is negative.
Show the answer and steps
- −3 × m = −3m.
- −3 × 4 = −12.
Answer: −3m − 12
Common mistakes
- Multiplying only the first term inside parentheses.
- Dropping the sign on a negative constant.
- Adding unlike terms after distributing.
Practice tips
- Draw two arrows from the outside factor to the inside terms.
- Check by substituting a small value for the variable.