Unit 23 Algebraic Manipulation

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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
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Unit 23 Algebraic Manipulation

• 23.1 Simultaneous Linear Equations

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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
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Then add the equations
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Hence
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Unit 23 Algebraic Manipulation

• 23.2 Expanding Brackets

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Expand Solution
(a)
(b)
(d)
(c)
(a)
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(d)
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(b)
(c)
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Unit 21Formula

• 23.3 Linear Factorisation

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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
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Unit 23 Algebraic Manipulation

• 23.4 Quadratic Factors 1

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Factorise
Solution This will be in the form of So If
the possible values are
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1 20 21
2 10 12
4 5 9
Which of these values satisfies
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Unit 23 Algebraic Manipulation

• 23.5 Quadratic Factors 2

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Factorise
Solution This must be in the form So and The
se are the possibilities if
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-1 3 5
3 -1 1
-3 1 -1
1 -3 -5
Hence and
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