1. Background Knowledge By the end of this lesson you will be able to explain/solve the following: 1.Difference of Two Squares 2.Perfect Squares 3.Sum & Product Type

2. Factorisation Algebraic factorisation is the reverse process of expansion

3. Factorisation

4. Worked Example 13

5. Exercise H

6. Worked Example 14

7. Exercise H

8. Factorisation By ‘Splitting’ The X-term An expression with three terms is called a trinomial. Quadratic trinomials can be written in the form: ax 2 + bx + c where the highest power is a squared term. To factorise a quadratic trinomial: factor pair of ac sum of b a) identify the factor pair of ac that has a sum of b breaking the x-term into two b) rewrite the expression by breaking the x-term into two terms using the factor pair from the previous step grouping c) factorise the resulting expression by grouping.

9. Worked Example

10. Exercise H

11. Worked Example 16

12. Exercise H

13. Worked Example 17

14. Exercise H

15. Completing the Square Consider factorising x 2 − 8x + 5 Can you find factors of 5 that add to −8? There are no integer factors but there are factors So far we have factorised quadratic trinomials where the factors have involved integers There are cases, however, where not only rational numbers are used, but also irrational numbers such as surds

16. Worked Example

18. Completing the Square