Factorising Algebraic Expressions

Factorising Algebraic Expressions
with common factors of numbers and pronumerals

​Example: Factorise 12ab+18b

To factorise an expression that contains both numbers and pronumerals, we first find the HCF of the numbers and then find the HCF of the pronumerals.
* Remember, a pronumeral represents a number, so these can be factorised.

Multiple Choice

What is the highest common factor of 12 and 18?

• 12

• 2

• 6

• 18

Multiple Choice

What is the highest common factor of ab and b?

• ab

• a

• b

Multiply 6 and b, then separate the other factors

6bx2a = 12ab and 6bx3 = 18b
this becomes 6bx 2a + 6b x 3
Take out the HCF and bracket the remaining factors to get:
6b(2a+3)

Example 2

​Expressions with an index

Math Response

What is the HCF of 8 and 12?

Type answer here

Correct Answer: 4

Deg^°

Rad

Math Response

What is the HCF of $$x^2\ and\ x$$ ?

Type answer here

Correct Answer: x

Deg^°

Rad

​Multiplying together and factorising:

8x² + 12x = 4x(2x + 3)

Note: you can check your answer by expanding the brackets; you should get the original question