1. 3: Quadratic Expressions Expanding Brackets and
“Teach A Level Maths” Vol. 1: AS Core Modules
3: Quadratic Expressions Expanding Brackets and
Factorisation
© Christine Crisp

2. Module C1
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3. Expanding Quadratic Expressions
e.g. 1
A square of a quantity means multiply by itself
e.g. 2

4. Exercises 1. 2. 3. 4.

5. so, x is a factor of both terms. It is a common factor
Factorising
Method 1: Common Factors
e.g.
means
so, x is a factor of both terms. It is a common factor
So,
Common factor

6. Factorise the following by taking out the common factors
Exercises
Factorise the following by taking out the common factors 1. 2. 3.

7. 4. 5. 6. 7. 8.

8. Method 2: The difference of two squares
Factorising
Method 2: The difference of two squares
(Square roots)
e.g.1
A minus sign
Another square
One square
e.g.2

9. Can’t do it! It’s NOT a difference
Exercises 1. 2.
Common factor first! 3.
Think! 4.
What about ?
Can’t do it! It’s NOT a difference

10. –3x is called the linear term
Factorising
Method 3: Trinomials
e.g. 1 or
The factors could not give 3 for the coefficient of x, so we try
We need –3x so we want – 4x and +1x.
–3x is called the linear term

11. Signs of factors are the same
Method 3: Trinomials
e.g. 2
Constant positive 
Signs of factors are the same

12. Signs of factors are the same
Exercises
Constant positive 
Signs of factors are the same 1. 2 3 2. 2 3 3 4 3.

13. Signs of factors are different
Exercises
Constant negative 
Signs of factors are different 4. 1 6 6 5. 1 6. 1 3

14. Exercises 7. 8. 9.
10.
11.
12.

15. SUMMARY There are 3 methods of factorising quadratic expressions.
Common factors.
The difference of 2 squares.
Trinomial factors.
List possible pairs of factors of the constant.
Constant term positive signs are the same.
Constant term negative one sign is positive and one is negative.
Choose a pair of factors of the constant and check the linear term is correct. If not, try again.

16. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

17. SUMMARY
There are 3 methods of factorising quadratics.
Common factors.
The difference of 2 squares.
Trinomial factors.
List possible pairs of factors of the constant.
Constant term positive signs are the same.
Constant term negative one sign is positive and one is negative.
Choose a pair of factors of the constant and check the linear term is correct. If not, try again.

18. Examples 1. 2. 3. 4. 5. 6. 7. 8. 9.
10.

19. Examples
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.