The Distributive Law
The distributive law states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the results: a(b + c) = ab + ac.
What You Need to Know
Key Concept Diagram
The distributive law: a(b + c) = ab + ac and a(b − c) = ab − ac
Use the distributive law to expand brackets in algebraic expressions
Factorising is the reverse: find a common factor and write it outside the brackets
The distributive law is also used for mental multiplication, e.g. 7 x 18 = 7(10 + 8) = 70 + 56 = 126
Key Vocabulary
Distributive law
The rule a(b + c) = ab + ac; multiply the factor outside the bracket by each term inside
Expand
To remove brackets by multiplying out, e.g. 3(x + 4) = 3x + 12
Factorise
To write an expression as a product of its factors, the reverse of expanding
Common factor
A number or term that divides exactly into each term of an expression
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Expand: 4(3x + 5)
Question 2
Use the distributive law to calculate 6 x 23 mentally.
Question 3
Factorise: 15x + 10
Key Concepts Summary
- ●The distributive law: a(b + c) = ab + ac and a(b − c) = ab − ac
- ●Use the distributive law to expand brackets in algebraic expressions
- ●Factorising is the reverse: find a common factor and write it outside the brackets
- ●The distributive law is also used for mental multiplication, e.g. 7 x 18 = 7(10 + 8) = 70 + 56 = 126