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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Factorising into a single bracket

Taking out a common factor.

16 original questions, 57 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

Factorise

  1. 8x − 12
  2. 14 + 21y
2 marks
Show answer
a) 4(2x - 3) b) 7(2 + 3y)
2

Factorise fully

  1. x2 + 7x
  2. 5p2 − 5p
2 marks
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a) x(x + 7) b) 5p(p - 1)
3
  1. Expand 4(2x − 5)
  2. Factorise 6y + 15
2 marks
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a) 8x - 20 b) 3(2y + 5)
4

Mia says that 12x − 18 = 3(4x − 6).

  1. Expand 3(4x − 6) to check that she is right.
  2. Mia has not factorised fully. Write 12x − 18 fully factorised.
3 marks
Show answer
a) 3(4x - 6) = 12x - 18, so she is right b) 6(2x - 3)
5

Factorise 6x − 15. Hence, or otherwise, solve 6x − 15 = 3.

3 marks
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3(2x - 5); x = 3
6
  1. Expand and simplify 3(x + 4) + 2(x − 1).
  2. Factorise your answer to part (a).
  3. Solve 3(x + 4) + 2(x − 1) = 30.
4 marks
Show answer
a) 5x + 10 b) 5(x + 2) c) x = 4
7
  1. Factorise 5x + 20
  2. Factorise x2 − 9x
2 marks
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a) 5(x + 4) b) x(x - 9)
8

Factorise 4x + 12. Hence, or otherwise, solve 4x + 128 = 5.

3 marks
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4(x + 3); x = 7
9

Factorise fully 10x − 25. Hence solve the inequality 10x − 25 < 15. Describe how you would show your answer on a number line.

4 marks
Show answer
5(2x - 5); x < 4; open circle at 4 with the arrow pointing left
10
  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
Show answer
a) He only multiplied the first term by 3; 3 times 4 = 12, so the answer should be 6x + 12 b) 6x(2x + 3)
11

The area of a rectangle is (12x2 + 18x) cm2. The width of the rectangle is 6x cm.

Factorise 12x2 + 18x fully and use it to find an expression for the length of the rectangle.

4 marks
Show answer
6x(2x + 3); length = (2x + 3) cm
12
  1. Expand and simplify (y − 3)(y − 8)
  2. Factorise fully 4a2b + 6ab2
4 marks
Show answer
a) y2 - 11y + 24 b) 2ab(2a + 3b)
13
  1. Expand and simplify 5(2x + 1) − 3(x − 4)
  2. Factorise fully 18x2 − 27x
  3. Simplify (p2)5
5 marks
Show answer
a) 7x + 17 b) 9x(2x - 3) c) p10
14
  1. Solve 2(3x + 4) = 5x + 17
  2. Factorise fully 6y2 + 9y
4 marks
Show answer
a) x = 9 b) 3y(2y + 3)
15
  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
16
  1. Expand and simplify (2x + 3)(x + 4)
  2. Factorise fully 10y2 − 15y
  3. Solve 4(2x − 1) = 3x + 16
6 marks
Show answer
a) 2x2 + 11x + 12 b) 5y(2y - 3) c) x = 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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