​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.

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

​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