GCSEMathsEdexcelHigherExam Questions2. AlgebraExpanding Brackets

Expanding Brackets (Edexcel GCSE Maths: Higher): Exam Questions

Exam code: 1MA1

2 hours57 questions
Easy
Medium
Hard
1
1 mark

Expand    3 left parenthesis 2 y space minus space 5 right parenthesis

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2a
1 mark

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

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2b
2 marks

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

How did you do?

3a
1 mark

Expand       3 open parentheses 2 plus t close parentheses

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3b
2 marks

Expand    3 x open parentheses 2 x plus 5 close parentheses

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4
1 mark

Expand      4 open parentheses x plus 2 close parentheses

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5
1 mark

Expand       2 m open parentheses m plus 3 close parentheses

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6
2 marks

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

How did you do?

7a
1 mark

Expand      x open parentheses x plus 2 close parentheses

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7b
2 marks

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

How did you do?

8
1 mark

Expand      space x left parenthesis x minus 3 right parenthesis

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9
2 marks

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

How did you do?

10
1 mark

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

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11
2 marks

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

How did you do?

12
1 mark

Expand    7 left parenthesis x plus 5 right parenthesis

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13
2 marks

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

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14
1 mark

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

  • 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

Choose your answer

15
1 mark

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

  • 2 x

  • negative 2 x

  • 22 x

  • negative 22 x

Choose your answer

16
2 marks

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

How did you do?

1
2 marks

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

How did you do?

2
2 marks

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

How did you do?

3
2 marks

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

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4
2 marks

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

How did you do?

5
2 marks

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

How did you do?

6
2 marks

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

How did you do?

7
2 marks

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

How did you do?

8
2 marks

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

How did you do?

9
2 marks

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

How did you do?

10
2 marks

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

How did you do?

11
2 marks

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

How did you do?

12
2 marks

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

How did you do?

13
2 marks

Expand and simplify               open parentheses w minus 5 close parentheses squared

How did you do?

14
2 marks

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

How did you do?

15
2 marks

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

How did you do?

16
2 marks

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

How did you do?

17
2 marks

Expand and simplify

open parentheses 3 y minus z close parentheses open parentheses 2 y plus 5 z close parentheses

How did you do?

18
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2 marks

Expand and simplify open parentheses p plus 6 close parentheses open parentheses p minus 2 close parentheses

How did you do?

19
3 marks

A cube has a side length of open parentheses x plus 5 close parentheses space cm. Show that the volume V of the cube, in cm cubed, can be written as V equals x cubed plus 15 x squared plus 75 x plus 125.

How did you do?

1
3 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.

How did you do?

2
3 marks

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.

How did you do?

3
3 marks

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

How did you do?

4a
3 marks

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.

How did you do?

4b
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3 marks

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

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5
3 marks
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

How did you do?

6
3 marks

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

How did you do?

7
3 marks

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 = .............................................................

How did you do?

8
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3 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 ......................................

How did you do?

9
3 marks

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.

How did you do?

10
3 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

How did you do?

11
1 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

How did you do?

12
3 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.

How did you do?

13
3 marks

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

How did you do?

14
2 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.

How did you do?

15
3 marks

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.

How did you do?

16
3 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

How did you do?

17
4 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

How did you do?

18
4 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

How did you do?

19
3 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

How did you do?

20
4 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 = ..................

How did you do?

21
4 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

How did you do?

22
2 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.....................................................

How did you do?