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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 1 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 Factorising Expressions (Common Factors) Worksheet — Level 1 — Practice Set 3 — Answers

Find the highest common factor of the terms and write it outside the brackets.

1.Factorise fully: 35x − 56

Answer: 7(5x − 8)

  1. Highest common factor: 7
  2. 35x − 56 = 7(5x − 8)
  3. Check by expanding the brackets.
2.Factorise fully: 9x + 18

Answer: 9(x + 2)

  1. Highest common factor: 9
  2. 9x + 18 = 9(x + 2)
  3. Check by expanding the brackets.
3.Factorise fully: 16x − 36

Answer: 4(4x − 9)

  1. Highest common factor: 4
  2. 16x − 36 = 4(4x − 9)
  3. Check by expanding the brackets.
4.Factorise fully: 30x − 36

Answer: 6(5x − 6)

  1. Highest common factor: 6
  2. 30x − 36 = 6(5x − 6)
  3. Check by expanding the brackets.
5.Factorise fully: 6x − 42

Answer: 6(x − 7)

  1. Highest common factor: 6
  2. 6x − 42 = 6(x − 7)
  3. Check by expanding the brackets.
6.Factorise fully: 6x + 27

Answer: 3(2x + 9)

  1. Highest common factor: 3
  2. 6x + 27 = 3(2x + 9)
  3. Check by expanding the brackets.
7.Factorise fully: 7x − 7

Answer: 7(x − 1)

  1. Highest common factor: 7
  2. 7x − 7 = 7(x − 1)
  3. Check by expanding the brackets.
8.Factorise fully: 3x + 18

Answer: 3(x + 6)

  1. Highest common factor: 3
  2. 3x + 18 = 3(x + 6)
  3. Check by expanding the brackets.
9.Factorise fully: 6x + 21

Answer: 3(2x + 7)

  1. Highest common factor: 3
  2. 6x + 21 = 3(2x + 7)
  3. Check by expanding the brackets.
10.Factorise fully: 16x − 12

Answer: 4(4x − 3)

  1. Highest common factor: 4
  2. 16x − 12 = 4(4x − 3)
  3. Check by expanding the brackets.
11.Factorise fully: 24x − 64

Answer: 8(3x − 8)

  1. Highest common factor: 8
  2. 24x − 64 = 8(3x − 8)
  3. Check by expanding the brackets.
12.Factorise fully: 24x + 28

Answer: 4(6x + 7)

  1. Highest common factor: 4
  2. 24x + 28 = 4(6x + 7)
  3. Check by expanding the brackets.
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