1. Unit 23 Algebraic Manipulation
Presentation 1
Simultaneous Linear Equations
Presentation 2
Expanding Brackets
Presentation 3
Linear Factorisation
Presentation 4
Quadratic Factors 1
Presentation 5
Quadratic Factors 2

2. 23.1 Simultaneous Linear Equations
Unit 23 Algebraic Manipulation
23.1 Simultaneous Linear Equations

3. Solve the pair of simultaneous equations
Problem
Solve the pair of simultaneous equations
Solution
In order to be able to eliminate x, we multiply the first equation by 4 and the second by 3, to give
So if y = -2 we substitute back to find x, y ? ? ? ? ?
Then add the equations ? ? ? ? ? ?
Hence ? ?

4. Unit 23 Algebraic Manipulation
23.2 Expanding Brackets

5. Expand Solution (a) (b) (c) (d) (a) (b) (d) (c) ? ? ? ? ? ? ? ? ? ? ?

6. Unit 21 Formula
23.3 Linear Factorisation

7. (a) This is the reverse of the process of expanding.
Factorise
(a)
(b)
Solution
(a) This is the reverse of the process of expanding.
As 2 is a common factor of both terms,
(b) The common factor of and is ? ? ? ? ? ? ? ? ?

8. Unit 23 Algebraic Manipulation
23.4 Quadratic Factors 1

9. This will be in the form of
Factorise
Solution
This will be in the form of So
If the possible values are ? ? ?
Which of these values satisfies 1 20 21 2 10 12 4 5 9 ? ? ? ? ? ? ? ? ? ? ?

10. Unit 23 Algebraic Manipulation
23.5 Quadratic Factors 2

11. These are the possibilities if
Factorise
Solution
This must be in the form
So and
These are the possibilities if ? ? ? -1 3 5 1 -3 -5
Hence and ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?