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

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

4. Quadratic Expressions 1. 3. 2. 4. Exercises

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

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

7. Quadratic Expressions 4. 5. 6. 7. 8.

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

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

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

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

12. Quadratic Expressions Constant positive  Signs of factors are the same 1. 2. 3. 2 3 32 34 Exercises

13. Quadratic Expressions Constant negative  Signs of factors are different 4. 5. 6. 1 6 6 1 31 Exercises

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

15. Quadratic Expressions SUMMARY There are 3 methods of factorising quadratic expressions.  Common factors.  The difference of 2 squares.  Trinomial factors. 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. List possible pairs of factors of the constant.

16. Quadratic Expressions

17. 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.

18. Quadratic Expressions SUMMARY There are 3 methods of factorising quadratics.  Common factors.  The difference of 2 squares.  Trinomial factors. 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. List possible pairs of factors of the constant.

19. Quadratic Expressions Examples 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

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