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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 10 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Algebraic Expressions

Year 10 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: 9x − 45y

Answer: 9(x − 5y)

  1. Highest common factor: 9
  2. 9x − 45y = 9(x − 5y)
  3. Check by expanding the brackets.
2.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.
3.Factorise fully: 28a + 7b

Answer: 7(4a + b)

  1. Highest common factor: 7
  2. 28a + 7b = 7(4a + b)
  3. Check by expanding the brackets.
4.Factorise fully: 16x2 + 36x

Answer: 4x(4x + 9)

  1. Highest common factor: 4x
  2. 16x2 + 36x = 4x(4x + 9)
  3. Check by expanding the brackets.
5.Factorise fully: 25m + 45n

Answer: 5(5m + 9n)

  1. Highest common factor: 5
  2. 25m + 45n = 5(5m + 9n)
  3. Check by expanding the brackets.
6.Factorise fully: 15x2 − 24x

Answer: 3x(5x − 8)

  1. Highest common factor: 3x
  2. 15x2 − 24x = 3x(5x − 8)
  3. Check by expanding the brackets.
7.Factorise fully: 12x − 54y

Answer: 6(2x − 9y)

  1. Highest common factor: 6
  2. 12x − 54y = 6(2x − 9y)
  3. Check by expanding the brackets.
8.Factorise fully: 30x2 − 42x

Answer: 6x(5x − 7)

  1. Highest common factor: 6x
  2. 30x2 − 42x = 6x(5x − 7)
  3. Check by expanding the brackets.
9.Factorise fully: 4m − 4n

Answer: 4(m − n)

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

Answer: 6x(x − 8)

  1. Highest common factor: 6x
  2. 6x2 − 48x = 6x(x − 8)
  3. Check by expanding the brackets.
11.Factorise fully: 25x + 10y

Answer: 5(5x + 2y)

  1. Highest common factor: 5
  2. 25x + 10y = 5(5x + 2y)
  3. Check by expanding the brackets.
12.Factorise fully: 5x2 − 9x

Answer: x(5x − 9)

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