# Unit 8 Section 3 : Common Factors & Factorising

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

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Important note on answering factorisation questions
It is important to make sure that you answer factorisation questions in
the correct way, or the computer may not mark your question correctly.

 Please follow the following rules: ExampleQuestion RightAnswer WrongAnswer · do not put any spaces in your answer 5x + 35 = · always put the common factor first, then the brackets 7x + 14y = · keep the order of the terms the same as in the question 6xy + 9x² = · do not use 1x or 1y instead of x or y 4x + 12 = · do not put more than one sign between terms 4xy - 6x = · make sure the expression is fully factorised 10xy + 15x = · letters within terms should be in alphabetical order 10p²q + 15pq² =

Question 1
Factorise:
 (a) 2x + 4 = (b) 5x + 15 = (c) 6x + 18 = (d) 5x - 25 = (e) 3x - 21 = (f) 7x + 35 = (g) 9x - 12 = (h) 15x + 20 = (i) 42x + 15 =
Question 2
Factorise:
 (a) 3x² + 2x = (b) 5x² + 10x = (c) 6x - 3x² = (d) 6x² - 4x = (e) 21x² + 14x = (f) 15x - 25x² =
Question 3
Factorise:
 (a) xy + xz = (b) xyz + 3yz = (c) 4pq - 8qr = (d) 5xyz + 20uxy = (e) 5xy - 4py = (f) 7xy + 12xz =
Question 4
Factorise:
 (a) x²y + xy² = (b) 5x²y - 35xy = (c) 22xy + 4xy² = (d) x²yz + xy²z =
Question 5
Factorise:
 (a) 3x + 9y + 18z = (b) 4x² + 2x + 8xy = (c) 6x - 3xy + 12xz = (d) 5xz + 20x - 35xy = (e) 7x² + 14xy - 21xyz = (f) 4x + 6xz + 15xy =

You have now completed Unit 8 Section 3
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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