IGCSE Edexcel Maths 2 hours 49 questions
Expanding Brackets
Expanding Single Brackets / Expanding Multiple Brackets
Easy (16 questions) /27 Scan here for your answers
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Medium (16 questions) /32
Hard (17 questions) /54
Total Marks /113
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Easy Questions
1 Expand 3(2y − 5)
(1 mark)
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2 (a) Expand 4(3x + 5)
(1 mark)
(b) Expand and simplify 2(x − 4) + 3(x + 5)
(2 marks)
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3 (a) Expand 3(2 + t )
(1 mark)
(b) Expand 3x (2x + 5)
(2 marks)
4 Expand 4(x + 2)
(1 mark)
5 Expand 2 m ( m + 3)
(1 mark)
6 Expand and simplify 5(y − 2) + 2(y − 3)
(2 marks)
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7 (a) Expand x (x + 2)
(1 mark)
(b) Expand and simplify 3(y + 2) + 4(x − 1)
(2 marks)
8 Expand x (x − 3)
(1 mark)
9 Expand and simplify 3(y − 2) + 5(2y + 1)
(2 marks)
10 Expand 3y (4y − 3)
(1 mark)
11 Expand and simplify 3(x + 4) + 2(5x − 1)
(2 marks)
12 Expand 7(x + 5)
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(1 mark)
13 Expand 4t (3t – 2)
(2 marks)
14 Expand 4x 2 (3x + 5)
Circle your answer.
32x 3 12x 3 + 20x 2 7x 3 + 9x 2 12x 2 + 5
(1 mark)
15 (2x – 4) (3x + 5) is expanded and simplified.
Circle the term which is part of the answer.
2x −2x 22x −22x
(1 mark)
16 Multiply out and simplify (x − 8) 2
(2 marks)
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Medium Questions
1 Expand and simplify 3( m + 4) − 2(4m + 1)
(2 marks)
2 Expand and simplify 5(p + 3) − 2(1 − 2p )
(2 marks)
3 Expand and simplify (p + 9) (p − 4)
(2 marks)
4 Expand and simplify (x + 4) (x + 6)
(2 marks)
5 Expand and simplify ( m + 3) ( m + 10)
(2 marks)
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6 Expand and simplify (x − 5) (x + 3)
(2 marks)
7 Expand and simplify (y − 2) (y − 5)
(2 marks)
8 Expand and simplify (y + 2) (y + 5)
(2 marks)
9 Expand and simplify ( m + 7) ( m + 3)
(2 marks)
10 Expand and simplify (2x + 1) (x − 4)
(2 marks)
11 Expand and simplify ( 2x + 3 ) ( x − 8 )
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(2 marks)
12 Expand and simplify (2t − 3) (t + 5)
(2 marks)
13 Expand and simplify (w − 5) 2
(2 marks)
14 Expand and simplify (y + 4) (2 − y )
(2 marks)
15 Expand and simplify 3x (2x + 3) – x (3x + 5)
(2 marks)
16 Expand and simplify fully 4(2c + 3) – (5c – 1)
(2 marks)
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Hard Questions
1 Show that (x + 1) (x + 2) (x + 3) can be written in the form ax 3 + bx 2 + cx + d
where a , b , c and d are positive integers.
(3 marks)
2 Show that
(3x − 1) (x + 5) (4x − 3) = 12x 3 + 47x 2 − 62x + 15
for all values of x .
(3 marks)
3 Simplify fully ( a + 4b ) ( a − 2 b )
(3 marks)
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4 (a) Show that (2x + 1) (x + 3) (3x + 7) can be written in the form ax 3 + bx 2 + cx + d
where a , b , c and d are integers.
(3 marks)
9
(b) Solve (1 − x ) 2 <
25
(3 marks)
5 The area of square ABCD is 10 cm2.
Show that x 2 + 6x = 1
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(3 marks)
6 Expand and simplify 5x (x + 2) (3x − 4)
(3 marks)
7 Given that (8 − x ) (5 + x ) = y x + 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 = ............................................................
(3 marks)
8 Solve (2x + 5) 2 = (2x + 3) (2x – 1)
x= ......................................
(3 marks)
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9 The functions f and g are defined as
f (x ) = x 2 + 6
g(x ) = x – 10
Solve the equation fg(x ) = f (x )
Show clear algebraic working.
(3 marks)
10 Expand and simplify (4x + 1) (x – 3) (5x + 6)
(3 marks)
11 Show that x (x − 1) (x + 1) = x 3 − x
(1 mark)
12 Expand and simplify fully (x − 3) (x + 2) (x + 5)
(3 marks)
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13 Here is an identity.
a (3x – 10) ≡ 21x + 2b
Work out the values of a and b .
(3 marks)
14 (x + 5) (x + 2) (x + a ) ≡ x 3 + bx 2 + cx – 30
Work out the values of the integers a, b and c .
a = ......................
b = ......................
c = ......................
(3 marks)
15 Expand and simplify (3x 2 + 2) (2x + 5) – 6x (x 2 – 3)
(4 marks)
16 Expand and simplify.
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(x + 1) (x − 1) (x + 2)
(3 marks)
17 Expand and simplify.
(2x − 1) (x + 5) (3x − 2)
(4 marks)
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