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IGCSEMathsCambridge (CIE)International MathsExtendedExam QuestionsAlgebra & SequencesExpanding & Factorising Brackets

Expanding & Factorising Brackets (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

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Expanding & Factorising Brackets

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1
Sme Calculator1 mark

Factorise completely.

4 space minus space 8 x

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2
Sme Calculator2 marks

Factorise completely.

3 x squared minus 12 x y

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3
Sme Calculator2 marks

Expand and simplify left parenthesis x plus 7 right parenthesis left parenthesis x minus 3 right parenthesis space. 

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1a
Sme Calculator1 mark

Factorise.

x y plus 2 w x

1b
Sme Calculator2 marks

2 p x minus x plus 14 p minus 7

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2
Sme Calculator2 marks

Factorise completely.

3 a squared b space minus space a b squared

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3
Sme Calculator4 marks

Factorise completely.

i) 6 y squared space minus space 15 x y 

 [2]

ii) y to the power of 2 space end exponent minus space 9 x squared 

 [2]

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4
Sme Calculator1 mark

Factorise space x squared minus 25.

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5
Sme Calculator2 marks

Expand and simplify 5 open parentheses p plus 3 close parentheses minus 2 open parentheses 1 minus 2 p close parentheses

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6
Sme Calculator2 marks

Expand and simplify  open parentheses p plus 9 close parentheses open parentheses p minus 4 close parentheses

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1
Sme Calculator3 marks

Expand and simplify.

open parentheses x plus 7 y close parentheses open parentheses x minus y close parentheses open parentheses x minus 6 y close parentheses

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2
Sme Calculator2 marks

Factorise

2 x space plus space 6 space – space 3 x y space – space 9 y

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3
Sme Calculator2 marks

Factorise  24 space plus space 5 x space minus space x squared.

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4
Sme Calculator2 marks

Expand and simplify  open parentheses 3 x minus 5 y close parentheses open parentheses 2 x plus y close parentheses.

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5
Sme Calculator3 marks

Factorise  5 m squared minus 20 p to the power of 4.

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6
Sme Calculator2 marks

Factorise  12 a b cubed plus 18 a cubed b squared.

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7
Sme Calculator5 marks

Factorise.

i) 2 m n plus m squared minus 6 n minus 3 m

[2]

ii) 4 y squared minus 81

[1]

iii) t squared minus 6 t plus 8

[2]

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1
Sme Calculator3 marks

Expand and simplify.

open parentheses x minus 2 close parentheses open parentheses x plus 5 close parentheses open parentheses 2 x minus 1 close parentheses

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2
Sme Calculator3 marks

Write open parentheses x space plus space 1 close parentheses open parentheses x space minus space 3 close parentheses squared in the form a x to the power of 3 space end exponent plus space b x squared space plus space c x space plus space d.

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3
Sme Calculator3 marks

Expand and simplify.

left parenthesis y plus 3 right parenthesis left parenthesis y minus 4 right parenthesis left parenthesis 2 y minus 1 right parenthesis

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4
Sme Calculator6 marks

Factorise completely.

i) 15 p squared q squared minus 25 q cubed   

[2]

ii) 4 f g plus 6 g h plus 10 f k plus 15 h k   

[2]

iii) 81 k squared minus m squared   

[2]

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5
Sme Calculator2 marks

Factorise  3 x to the power of 2 space end exponent plus space 11 x space – space 20

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6
Sme Calculator3 marks

Factorise completely.

2 t squared minus 98 m squared

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