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Year 7 · Key Stage 3 · free KS3 maths worksheet

Simplifying and expanding

12 original questions, 28 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or 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

Simplify  7c − 2c + 4c

1 mark
Show answer
9c
2

Simplify  6x + 3y − 2x + 5y

2 marks
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4x + 8y
3
  1. Simplify  5 × 2m
  2. Simplify  n × n × n × n
  3. Simplify  3c × 4d
3 marks
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a) 10m b) n4 c) 12cd
4

Simplify

  1. 18p ÷ 6
  2. 4a × 5b
  3. 24xy ÷ 8y
3 marks
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a) 3p b) 20ab c) 3x
5
  1. Simplify  8x + 5 − 3x + 2
  2. Simplify  2g × 5g
3 marks
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a) 5x + 7 (accept 7 + 5x) b) 10g2
6

The sides of a triangle are (2a + 3) cm, (4a − 1) cm and (a + 5) cm.

Write an expression for the perimeter of the triangle. Give your answer in its simplest form.

4a − 1a + 52a + 3Diagram NOT accurately drawn
2 marks
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7a + 7
7

Expand

  1. 3(x + 4)
  2. 5(2y − 3)
  3. a(a + 6)
3 marks
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a) 3x + 12 b) 10y - 15 c) a2 + 6a
8

Oliver expands 4(3m − 2) and writes

4(3m − 2) = 12m − 2

Explain the mistake Oliver has made and write the correct answer.

2 marks
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He did not multiply the 2 by 4. Correct answer 12m - 8
9

Expand and simplify 2(x + 5) + 3(x + 1)

2 marks
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5x + 13
10

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
11

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

3 marks
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6a + 22
12

Amara makes a poster from two rectangles of card.

Rectangle A is 3 cm by (x + 4) cm.
Rectangle B is 5 cm by (2x − 1) cm.

Show that the total area of the card is (13x + 7) cm2.

x + 43A2x − 15BDiagram NOT accurately drawn
3 marks
Show answer
3(x + 4) + 5(2x - 1) = 3x + 12 + 10x - 5 = 13x + 7

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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