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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: 6m − 2n

Answer: 2(3m − n)

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

Answer: x(2x + 1)

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

Answer: 3(2a − b)

  1. Highest common factor: 3
  2. 6a − 3b = 3(2a − b)
  3. Check by expanding the brackets.
4.Factorise fully: 15x2 + 40x

Answer: 5x(3x + 8)

  1. Highest common factor: 5x
  2. 15x2 + 40x = 5x(3x + 8)
  3. Check by expanding the brackets.
5.Factorise fully: 4m − 18n

Answer: 2(2m − 9n)

  1. Highest common factor: 2
  2. 4m − 18n = 2(2m − 9n)
  3. Check by expanding the brackets.
6.Factorise fully: 10x2 + 12x

Answer: 2x(5x + 6)

  1. Highest common factor: 2x
  2. 10x2 + 12x = 2x(5x + 6)
  3. Check by expanding the brackets.
7.Factorise fully: 6x − 15y

Answer: 3(2x − 5y)

  1. Highest common factor: 3
  2. 6x − 15y = 3(2x − 5y)
  3. Check by expanding the brackets.
8.Factorise fully: 25x2 − 10x

Answer: 5x(5x − 2)

  1. Highest common factor: 5x
  2. 25x2 − 10x = 5x(5x − 2)
  3. Check by expanding the brackets.
9.Factorise fully: 28a − 63b

Answer: 7(4a − 9b)

  1. Highest common factor: 7
  2. 28a − 63b = 7(4a − 9b)
  3. Check by expanding the brackets.
10.Factorise fully: 20x2 + 35x

Answer: 5x(4x + 7)

  1. Highest common factor: 5x
  2. 20x2 + 35x = 5x(4x + 7)
  3. Check by expanding the brackets.
11.Factorise fully: 12x − 27y

Answer: 3(4x − 9y)

  1. Highest common factor: 3
  2. 12x − 27y = 3(4x − 9y)
  3. Check by expanding the brackets.
12.Factorise fully: 2x2 + 5x

Answer: x(2x + 5)

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