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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 2 — 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 2 — Practice Set 2 — Answers

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

1.Factorise fully: 6a + 2b

Answer: 2(3a + b)

  1. Highest common factor: 2
  2. 6a + 2b = 2(3a + b)
  3. Check by expanding the brackets.
2.Factorise fully: 8x2 + 14x

Answer: 2x(4x + 7)

  1. Highest common factor: 2x
  2. 8x2 + 14x = 2x(4x + 7)
  3. Check by expanding the brackets.
3.Factorise fully: 18x − 6y

Answer: 6(3x − y)

  1. Highest common factor: 6
  2. 18x − 6y = 6(3x − y)
  3. Check by expanding the brackets.
4.Factorise fully: 4x2 − 24x

Answer: 4x(x − 6)

  1. Highest common factor: 4x
  2. 4x2 − 24x = 4x(x − 6)
  3. Check by expanding the brackets.
5.Factorise fully: 15a + 18b

Answer: 3(5a + 6b)

  1. Highest common factor: 3
  2. 15a + 18b = 3(5a + 6b)
  3. Check by expanding the brackets.
6.Factorise fully: 5x2 − 10x

Answer: 5x(x − 2)

  1. Highest common factor: 5x
  2. 5x2 − 10x = 5x(x − 2)
  3. Check by expanding the brackets.
7.Factorise fully: 12a + 21b

Answer: 3(4a + 7b)

  1. Highest common factor: 3
  2. 12a + 21b = 3(4a + 7b)
  3. Check by expanding the brackets.
8.Factorise fully: 5x2 + 3x

Answer: x(5x + 3)

  1. Highest common factor: x
  2. 5x2 + 3x = x(5x + 3)
  3. Check by expanding the brackets.
9.Factorise fully: 9x − 9y

Answer: 9(x − y)

  1. Highest common factor: 9
  2. 9x − 9y = 9(x − y)
  3. Check by expanding the brackets.
10.Factorise fully: 4x2 + 32x

Answer: 4x(x + 8)

  1. Highest common factor: 4x
  2. 4x2 + 32x = 4x(x + 8)
  3. Check by expanding the brackets.
11.Factorise fully: 4a + 2b

Answer: 2(2a + b)

  1. Highest common factor: 2
  2. 4a + 2b = 2(2a + b)
  3. Check by expanding the brackets.
12.Factorise fully: x2 − 6x

Answer: x(x − 6)

  1. Highest common factor: x
  2. x2 − 6x = x(x − 6)
  3. Check by expanding the brackets.
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