Factorising Out Terms (Cambridge (CIE) IGCSE International Maths)
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
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Basic Factorising
What is factorisation?
A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)
3(x + 2) is factorised
It is 3 × (x + 2)
3x + 6 is not factorised
3xy is factorised
It is 3 × x × y
Numbers can also be factorised
12 = 2 x 2 x 3
In algebra, factorisation is the reverse of expanding brackets
It's putting it into brackets, rather than removing brackets
How do I factorise two terms?
To factorise 12x2 + 18x
Find the highest common factor of the number parts
6
Find the highest common factor of the algebra parts
x
Multiply both to get the overall highest common factor
6x
12x2 + 18x is the same as 6x × 2x + 6x × 3
Using the highest common factor
Take out the highest common factor
Write it outside a set of brackets
Put the remaining terms, 2x + 3, inside the brackets
This gives the answer
6x (2x + 3)
To factorise an expression containing multiple variables, e.g. 2a3b - 4a2b2
Use the same approach as above
Find the highest common factor of the number parts
2
Find the highest common factor of the algebra parts
a and b appear in both terms
The highest common factor of a3 and a2 is a2
The highest common factor of b and b2 is b
a2b
Multiply both to get the overall highest common factor
2a2b
2a3b - 4a2b2 is the same as 2a2b × a - 2a2b × 2b
Using the highest common factor
Take out the highest common factor
Write it outside a set of brackets
Put the remaining terms, a - 2b, inside the brackets
This gives the answer
2a2b (a - 2b)
Examiner Tips and Tricks
In the exam, check that your factorisation is correct by expanding the brackets!
Factorise mean factorise fully.
x (6x + 10) is not fully factorised but 2x (3x + 5) is.
Worked Example
(a) Factorise 5x + 15
Find the highest common factor of 5 and 15
5
There is no x in the second term, so no highest common factor in x is needed
Think of each term as 5 × something
5 × x + 5 × 3
Take out the 5 and put x + 3 in brackets
5(x + 3)
5(x + 3)
(b) Factorise fully 30x2 - 24x
Find the highest common factor of 30 and 24
6
Find the highest common factor of x2 and x
x
Find the overall highest common factor by multiplying these together
6x
Think of each term as 6x × something
6x × 5x - 6x × 4
Take out the 6x and put 5x - 4 in brackets
6x (5x - 4)
6x (5x - 4)
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