Lesson 11. Common factors

We know that

3(a + b)

is we same as

3a + 3b

so

3a + 3b = 3(a + b)

3 is a factor of both 3a and 3b

so 3 is the common factor of 3a and 3b

Common factors can be extracted from algebraic expressions.

Take out common factor 3.

This is called ‘factorising’

3a + 3b

EXAMPEL:

Factorise

7x – 7y

7x and 7y have common factor 7

so

7x – 7y = 7(x – y)

EXAMPEL:

Factorise

5a + 10b

5 divides into 5a and 10b

so 5a and 10b have common factor 5

so 5a + 10b = 5(a + 2b)

Letters as well as numbers can be the common factors.

EXAMPEL:

Factorise

ab + ac

ab and ac have common factor a

So

ab + ac = a(b + c)

multiply out to check the answer is correct

EXAMPEL:

Factorise

5ac + 15bc

5ac and 15bc have common factor 5c so

5ac + 15bc = 5c(a + 3b)

EXAMPEL:

Factorise

4x² – 6x

4x² and 6x have common factor 2x so

4x² – 6x = 2x(2x – 3) 

Lesson 11

•  Test 1 
•  Test 2
•  Test 3