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

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

1.Factorise fully: 12a + 20b

Answer: 4(3a + 5b)

  1. Highest common factor: 4
  2. 12a + 20b = 4(3a + 5b)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 − 16x

Answer: 2x(3x − 8)

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

Answer: 6(4m + n)

  1. Highest common factor: 6
  2. 24m + 6n = 6(4m + n)
  3. Check by expanding the brackets.
4.Factorise fully: 6x2 − 8x

Answer: 2x(3x − 4)

  1. Highest common factor: 2x
  2. 6x2 − 8x = 2x(3x − 4)
  3. Check by expanding the brackets.
5.Factorise fully: 6m − 48n

Answer: 6(m − 8n)

  1. Highest common factor: 6
  2. 6m − 48n = 6(m − 8n)
  3. Check by expanding the brackets.
6.Factorise fully: 4x2 + 5x

Answer: x(4x + 5)

  1. Highest common factor: x
  2. 4x2 + 5x = x(4x + 5)
  3. Check by expanding the brackets.
7.Factorise fully: 9a − 3b

Answer: 3(3a − b)

  1. Highest common factor: 3
  2. 9a − 3b = 3(3a − b)
  3. Check by expanding the brackets.
8.Factorise fully: 15x2 + 3x

Answer: 3x(5x + 1)

  1. Highest common factor: 3x
  2. 15x2 + 3x = 3x(5x + 1)
  3. Check by expanding the brackets.
9.Factorise fully: 12m + 32n

Answer: 4(3m + 8n)

  1. Highest common factor: 4
  2. 12m + 32n = 4(3m + 8n)
  3. Check by expanding the brackets.
10.Factorise fully: 6x2 + 3x

Answer: 3x(2x + 1)

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

Answer: 6(4m − 9n)

  1. Highest common factor: 6
  2. 24m − 54n = 6(4m − 9n)
  3. Check by expanding the brackets.
12.Factorise fully: 3x2 − 2x

Answer: x(3x − 2)

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