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Grade 3 · Foundation · free GCSE maths worksheet

Expanding a single bracket

Multiplying out 3(x + 4).

12 original questions, 35 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Expand  3(x + 4)

1 mark
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3x + 12
2

Expand  7(2p − 1)

2 marks
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14p - 7
3

Expand  −2(x − 5)

2 marks
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-2x + 10
4

Expand  p(p − 6)

2 marks
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p2 - 6p
5

Priya says that (5x − 3) − (2x − 7) = 3x − 10

Priya is wrong. Explain the mistake she has made.

1 mark
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She did not change the sign of -7 when subtracting; the answer should be 3x + 4
6
  1. Expand 4(2x − 5)
  2. Factorise 6y + 15
2 marks
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a) 8x - 20 b) 3(2y + 5)
7

Expand and simplify  2(3a + 1) + 4(a + 5)

3 marks
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10a + 22
8
  1. Sam expands 3(2x + 4) and gets the answer 6x + 4
    Explain the mistake Sam has made.
  2. Factorise fully 12x2 + 18x
3 marks
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a) He only multiplied the first term by 3; 3 times 4 = 12, so the answer should be 6x + 12 b) 6x(2x + 3)
9

A rectangle has a width of 4 cm and a length of (x + 7) cm.

  1. Write an expression for the area of the rectangle. Expand any brackets.
  2. The area of the rectangle is 60 cm2. Work out the value of x.
4 marks
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a) 4x + 28 b) 8
10
  1. Expand and simplify 3(x + 2) + 2(x − 5)
  2. Solve 5(x − 3) = 20
4 marks
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a) 5x - 4 b) x = 7
11
  1. Expand and simplify 5(2x + 1) − 3(x − 4)
  2. Factorise fully 18x2 − 27x
  3. Simplify (p2)5
5 marks
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a) 7x + 17 b) 9x(2x - 3) c) p10
12
  1. Expand 3x(2x − 5)
  2. Factorise fully 20a2b − 8ab
  3. Make x the subject of y = 4x − 7
6 marks
Show answer
a) 6x2 - 15x b) 4ab(5a - 2) c) x = (y + 7)/4

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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