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

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

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 ? ?

Unit 23 Algebraic Manipulation 23.2 Expanding Brackets

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

Unit 21 Formula 23.3 Linear Factorisation

(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 ? ? ? ? ? ? ? ? ?

Unit 23 Algebraic Manipulation 23.4 Quadratic Factors 1

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 ? ? ? ? ? ? ? ? ? ? ?

Unit 23 Algebraic Manipulation 23.5 Quadratic Factors 2

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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?