Definition: The distributive property says that multiplying a number by a sum equals multiplying it by each addend and adding the products: a(b + c) = ab + ac.
What is the distributive property?
It lets you spread multiplication over addition or subtraction. In symbols, a(b + c) = ab + ac and a(b – c) = ab – ac.
How does it speed up mental math?
To compute 7 x 98, think of 98 as 100 – 2. Then 7(100 – 2) = 700 – 14 = 686. A rectangle makes it visible: a rectangle 7 tall and 98 wide splits into 7 by 100 minus 7 by 2.
How is it used with variables?
Expand 4(3x + 5): multiply 4 by each term. You get 12x + 20. Going the other way is called factoring: 18 + 24y = 6(3 + 4y), since 6 is a common factor of 18 and 24.
What mistake should you avoid?
Multiplying only the first term. The expression 5(x + 8) is 5x + 40, not 5x + 8. Also watch signs: -3(y – 2) = -3y + 6, because the negative multiplies both terms.
Where to learn it
- Writing, Evaluating and Simplifying Algebraic Expressions – lesson
- Rewriting Linear Expressions in Equivalent Forms – lesson