As well as being able to remove brackets by expanding expressions, it is also important to
be able to write expressions so that they include brackets; this is called factorisation.
Example Question 1
Factorise 4x + 6.
The first stage is to find break up 4x and 6 into factors, so that you can find everything that goes into both 4x and 6.
In this case 2 is the highest factor of both 4x and 6, so 2 will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.
We can check the answer by multiplying out the brackets: 2(2x+3) = 4x+6
Example Question 2
Factorise 18n + 24.
The first stage is to find break up 18n and 24 into factors, so that you can find everything that goes into both 18n and 24.
In this case 6 is the highest factor of both 18n and 24, so 6 will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.
We can check the answer by multiplying out the brackets: 6(3n+4) = 18n+24
Example Question 3
Factorise 4x² + 6x.
In this case 2x is the highest factor of both 4x² and 6x, so 2x will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.
We can check the answer by multiplying out the brackets: 2x(2x+3) = 4x²+6x
Example Question 4
Factorise 3xy² + 12x²y.
In this case 3xy is the highest factor of both 3xy² and 12x²y, so 3xy will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.
We can check the answer by multiplying out the brackets: 3xy(y+4x) = 3xy² + 12x²y
Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Factorise 9x + 15
(b) Factorise 40x  10
(c) Factorise 10x² + 6x
(d) Factorise 15x²y+25xy
(e) Factorise 4pq²  20pq + 8p²q
