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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

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

1.Factorise fully: 3m + 3n

Answer: 3(m + n)

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

Answer: 2x(3x − 1)

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

Answer: 2(4m + 9n)

  1. Highest common factor: 2
  2. 8m + 18n = 2(4m + 9n)
  3. Check by expanding the brackets.
4.Factorise fully: 25x2 − 40x

Answer: 5x(5x − 8)

  1. Highest common factor: 5x
  2. 25x2 − 40x = 5x(5x − 8)
  3. Check by expanding the brackets.
5.Factorise fully: 9m + 54n

Answer: 9(m + 6n)

  1. Highest common factor: 9
  2. 9m + 54n = 9(m + 6n)
  3. Check by expanding the brackets.
6.Factorise fully: 24x2 + 20x

Answer: 4x(6x + 5)

  1. Highest common factor: 4x
  2. 24x2 + 20x = 4x(6x + 5)
  3. Check by expanding the brackets.
7.Factorise fully: 24a + 16b

Answer: 8(3a + 2b)

  1. Highest common factor: 8
  2. 24a + 16b = 8(3a + 2b)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 − 5x

Answer: x(6x − 5)

  1. Highest common factor: x
  2. 6x2 − 5x = x(6x − 5)
  3. Check by expanding the brackets.
9.Factorise fully: 12a + 6b

Answer: 6(2a + b)

  1. Highest common factor: 6
  2. 12a + 6b = 6(2a + b)
  3. Check by expanding the brackets.
10.Factorise fully: 12x2 − 9x

Answer: 3x(4x − 3)

  1. Highest common factor: 3x
  2. 12x2 − 9x = 3x(4x − 3)
  3. Check by expanding the brackets.
11.Factorise fully: 30x + 48y

Answer: 6(5x + 8y)

  1. Highest common factor: 6
  2. 30x + 48y = 6(5x + 8y)
  3. Check by expanding the brackets.
12.Factorise fully: 36x2 − 6x

Answer: 6x(6x − 1)

  1. Highest common factor: 6x
  2. 36x2 − 6x = 6x(6x − 1)
  3. Check by expanding the brackets.
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