GCSEMathsEdexcelHigherExam Questions2. AlgebraExpanding Brackets

Expanding Brackets (Edexcel GCSE Maths: Higher)

Exam Questions

2 hours54 questions
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1
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Expand    3 left parenthesis 2 y space minus space 5 right parenthesis

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2a
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Expand  4 left parenthesis 3 x plus thin space 5 right parenthesis

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2b
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Expand and simplify      2 open parentheses x minus 4 close parentheses space plus thin space 3 open parentheses x plus 5 close parentheses

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3a
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Expand       3 open parentheses 2 plus t close parentheses

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3b
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Expand    3 x open parentheses 2 x plus 5 close parentheses

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4
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Expand      4 open parentheses x plus 2 close parentheses

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5
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Expand       2 m open parentheses m plus 3 close parentheses

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6
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Expand and simplify      5 open parentheses y minus 2 close parentheses space plus space 2 open parentheses y minus 3 close parentheses

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7a
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Expand      x open parentheses x plus 2 close parentheses

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7b
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Expand and simplify        3 open parentheses y plus 2 close parentheses space plus thin space 4 open parentheses x minus 1 close parentheses

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8
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Expand      space x left parenthesis x minus 3 right parenthesis

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9
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Expand and simplify       3 open parentheses y minus 2 close parentheses space plus space 5 open parentheses 2 y plus 1 close parentheses

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10
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Expand     space 3 y left parenthesis 4 y space minus space 3 right parenthesis

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11
Sme Calculator2 marks

Expand and simplify       3 open parentheses x plus 4 close parentheses space plus space 2 open parentheses 5 x minus 1 close parentheses

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12
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Expand    7 left parenthesis x plus 5 right parenthesis

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13
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Expand  4 t left parenthesis 3 t space – space 2 right parenthesis

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14
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Expand 4 x squared space left parenthesis 3 x space plus space 5 right parenthesis

Circle your answer.

32 x cubed

12 x cubed space plus space 20 x squared

7 x cubed space plus space 9 x squared

12 x squared space plus space 5

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15
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left parenthesis 2 x space – space 4 right parenthesis left parenthesis 3 x space plus space 5 right parenthesis  is expanded and simplified.
Circle the term which is part of the answer.

2 x

negative 2 x

22 x

negative 22 x

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16
Sme Calculator2 marks

Multiply out and simplify open parentheses x minus 8 close parentheses squared

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1
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Expand and simplify       3 open parentheses m plus 4 close parentheses minus space 2 left parenthesis 4 m space plus space 1 right parenthesis

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

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3
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Expand and simplify     open parentheses p plus 9 close parentheses open parentheses p minus 4 close parentheses

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4
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Expand and simplify        left parenthesis x plus 4 right parenthesis left parenthesis x plus 6 right parenthesis

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5
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Expand and simplify  open parentheses m plus 3 close parentheses open parentheses m plus 10 close parentheses

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6
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Expand and simplify         open parentheses x minus 5 close parentheses open parentheses x plus 3 close parentheses

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7
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Expand and simplify            open parentheses y minus 2 close parentheses open parentheses y minus 5 close parentheses

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8
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Expand and simplify           open parentheses y plus 2 close parentheses open parentheses y plus 5 close parentheses

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9
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Expand and simplify        open parentheses m plus 7 close parentheses open parentheses m plus 3 close parentheses

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10
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Expand and simplify                        open parentheses 2 x plus 1 close parentheses open parentheses x minus 4 close parentheses

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11
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Expand and simplify      open parentheses 2 x plus 3 close parentheses open parentheses x minus 8 close parentheses

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12
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Expand and simplify                open parentheses 2 t minus 3 close parentheses open parentheses t plus 5 close parentheses

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13
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Expand and simplify               open parentheses w minus 5 close parentheses squared

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14
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Expand and simplify  open parentheses y plus 4 close parentheses open parentheses 2 minus y close parentheses

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15
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Expand and simplify  3 x left parenthesis 2 x space plus space 3 right parenthesis space – space x left parenthesis 3 x space plus space 5 right parenthesis

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16
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Expand and simplify fully  4 left parenthesis 2 c space plus space 3 right parenthesis space – space left parenthesis 5 c space – space 1 right parenthesis

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1
Sme Calculator3 marks

Show that left parenthesis x space plus space 1 right parenthesis left parenthesis x space plus space 2 right parenthesis left parenthesis x space plus space 3 right parenthesis can be written in the form a x cubed space plus space b x squared space plus space c x plus space d where  a comma space b comma space c and d are positive integers.

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2
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Show that

open parentheses 3 x minus 1 close parentheses open parentheses x plus 5 close parentheses open parentheses 4 x minus 3 close parentheses space equals space 12 x cubed space plus space 47 x squared space minus space 62 x space plus space 15

for all values of x.

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3
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Simplify fully open parentheses square root of a plus square root of 4 b end root space close parentheses open parentheses square root of a minus 2 square root of b close parentheses

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4a
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Show that left parenthesis 2 x space plus space 1 right parenthesis left parenthesis x space plus space 3 right parenthesis left parenthesis 3 x space plus space 7 right parenthesis can be written in the form a x cubed space plus space b x squared space plus space c x space plus space d   where a comma space b comma space c and d are integers.

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4b
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Solve           open parentheses 1 minus x close parentheses squared space less than space 9 over 25

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5
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q5-hard-2-3-expanding-brackets-edexcel-gcse-maths

The area of square A B C D is 10 cm2.
Show that x squared plus space 6 x space equals space 1

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6
Sme Calculator3 marks

Expand and simplify            5 x open parentheses x plus 2 close parentheses open parentheses 3 x minus 4 close parentheses

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7
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Given that open parentheses 8 minus square root of x close parentheses open parentheses 5 plus square root of x close parentheses equals y square root of x plus 21  where x is a prime number and y is an integer, find the value of x and the value of y. Show each stage of your working clearly.

x = .............................................................
y = .............................................................

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8
Sme Calculator3 marks

Solve left parenthesis 2 x space plus space 5 right parenthesis squared space space equals space left parenthesis 2 x space plus space 3 right parenthesis left parenthesis 2 x space – space 1 right parenthesis

x space equals ......................................

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9
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The functions space straight fand straight g are defined as

table row cell straight f left parenthesis x right parenthesis space end cell equals cell space x squared space plus space 6 space end cell row cell straight g left parenthesis x right parenthesis space end cell equals cell space x space – space 10 end cell end table

Solve the equation fg left parenthesis x right parenthesis space equals space straight f left parenthesis x right parenthesis

Show clear algebraic working.

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10
Sme Calculator3 marks

Expand and simplify left parenthesis 4 x space plus space 1 right parenthesis left parenthesis x space – space 3 right parenthesis left parenthesis 5 x space plus space 6 right parenthesis

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11
Sme Calculator1 mark

Show that x left parenthesis x space minus space 1 right parenthesis space open parentheses x space plus space 1 close parentheses equals space x cubed space minus space x

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12
Sme Calculator3 marks

left parenthesis x space plus space a right parenthesis left parenthesis x space plus space 3 a right parenthesis space identical to space x squared space plus space b x space plus space 75 space space

Work out the two possible values of b.

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13
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Expand and simplify fully open parentheses x minus 3 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 5 close parentheses

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14
Sme Calculator2 marks

s andspace t spaceare positive integers.

left parenthesis x space plus space s right parenthesis left parenthesis x space – space t right parenthesis is expanded and simplified.
The answer is x squared space plus space k x space – space 40 where k is a positive integer.

Work out the smallest possible value of k.

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15
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Here is an identity.

a left parenthesis 3 x space – space 10 right parenthesis space identical to space 21 x space plus space 2 b

Work out the values of a and b.

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16
Sme Calculator3 marks

left parenthesis x space plus space 5 right parenthesis left parenthesis x space plus space 2 right parenthesis left parenthesis x space plus space a right parenthesis space identical to space x to the power of 3 space end exponent plus space b x squared space plus space c x space – space 30

Work out the values of the integers space a comma space b spaceand c.

table row cell a space end cell equals cell space space...................... end cell row cell b space end cell equals cell space space...................... end cell row cell c space end cell equals cell space space...................... end cell end table

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17
Sme Calculator4 marks

Expand and simplify left parenthesis 3 x squared space plus space 2 right parenthesis left parenthesis 2 x space plus space 5 right parenthesis space – space 6 x left parenthesis x squared space – space 3 right parenthesis

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18
Sme Calculator4 marks

Expand and simplify   left parenthesis x space minus space 4 right parenthesis left parenthesis 2 x space plus space 3 y right parenthesis squared

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19
Sme Calculator3 marks

Expand and simplify.

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

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20
Sme Calculator4 marks

open parentheses x plus a close parentheses open parentheses x plus 3 close parentheses open parentheses 2 x plus 1 close parentheses space equals space b x cubed space plus space c x squared space plus space d x space minus 12

Find the value of a comma b, c and d.

a = ..................

b = ..................

c = ..................

d = ..................

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21
Sme Calculator4 marks

Expand and simplify.

left parenthesis 2 x space minus space 1 right parenthesis left parenthesis x space plus space 5 right parenthesis left parenthesis 3 x space minus space 2 right parenthesis

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22
Sme Calculator2 marks

open parentheses x plus 3 close parentheses open parentheses x minus 4 close parentheses open parentheses x plus 5 close parentheses is identical to x cubed plus a x squared minus 17 x plus b

Find the value of a and the value of b.

a space equals space..................................................... space b space equals space.....................................................

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