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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: 4a − 6b

Answer: 2(2a − 3b)

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

Answer: 2x(4x − 9)

  1. Highest common factor: 2x
  2. 8x2 − 18x = 2x(4x − 9)
  3. Check by expanding the brackets.
3.Factorise fully: 32m − 24n

Answer: 8(4m − 3n)

  1. Highest common factor: 8
  2. 32m − 24n = 8(4m − 3n)
  3. Check by expanding the brackets.
4.Factorise fully: 6x2 + 4x

Answer: 2x(3x + 2)

  1. Highest common factor: 2x
  2. 6x2 + 4x = 2x(3x + 2)
  3. Check by expanding the brackets.
5.Factorise fully: 14m + 35n

Answer: 7(2m + 5n)

  1. Highest common factor: 7
  2. 14m + 35n = 7(2m + 5n)
  3. Check by expanding the brackets.
6.Factorise fully: 2x2 + 16x

Answer: 2x(x + 8)

  1. Highest common factor: 2x
  2. 2x2 + 16x = 2x(x + 8)
  3. Check by expanding the brackets.
7.Factorise fully: 20x − 28y

Answer: 4(5x − 7y)

  1. Highest common factor: 4
  2. 20x − 28y = 4(5x − 7y)
  3. Check by expanding the brackets.
8.Factorise fully: 3x2 − 12x

Answer: 3x(x − 4)

  1. Highest common factor: 3x
  2. 3x2 − 12x = 3x(x − 4)
  3. Check by expanding the brackets.
9.Factorise fully: 40a + 64b

Answer: 8(5a + 8b)

  1. Highest common factor: 8
  2. 40a + 64b = 8(5a + 8b)
  3. Check by expanding the brackets.
10.Factorise fully: 2x2 − 12x

Answer: 2x(x − 6)

  1. Highest common factor: 2x
  2. 2x2 − 12x = 2x(x − 6)
  3. Check by expanding the brackets.
11.Factorise fully: 42x − 7y

Answer: 7(6x − y)

  1. Highest common factor: 7
  2. 42x − 7y = 7(6x − y)
  3. Check by expanding the brackets.
12.Factorise fully: 20x2 − 45x

Answer: 5x(4x − 9)

  1. Highest common factor: 5x
  2. 20x2 − 45x = 5x(4x − 9)
  3. Check by expanding the brackets.
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