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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 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: 5m + 25n

Answer: 5(m + 5n)

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

Answer: 3x(3x + 4)

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

Answer: 3(2m + n)

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

Answer: 5x(x + 6)

  1. Highest common factor: 5x
  2. 5x2 + 30x = 5x(x + 6)
  3. Check by expanding the brackets.
5.Factorise fully: 35x − 28y

Answer: 7(5x − 4y)

  1. Highest common factor: 7
  2. 35x − 28y = 7(5x − 4y)
  3. Check by expanding the brackets.
6.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.
7.Factorise fully: 28m − 21n

Answer: 7(4m − 3n)

  1. Highest common factor: 7
  2. 28m − 21n = 7(4m − 3n)
  3. Check by expanding the brackets.
8.Factorise fully: 10x2 + 45x

Answer: 5x(2x + 9)

  1. Highest common factor: 5x
  2. 10x2 + 45x = 5x(2x + 9)
  3. Check by expanding the brackets.
9.Factorise fully: 10m + 35n

Answer: 5(2m + 7n)

  1. Highest common factor: 5
  2. 10m + 35n = 5(2m + 7n)
  3. Check by expanding the brackets.
10.Factorise fully: 12x2 + 28x

Answer: 4x(3x + 7)

  1. Highest common factor: 4x
  2. 12x2 + 28x = 4x(3x + 7)
  3. Check by expanding the brackets.
11.Factorise fully: 12m + 54n

Answer: 6(2m + 9n)

  1. Highest common factor: 6
  2. 12m + 54n = 6(2m + 9n)
  3. Check by expanding the brackets.
12.Factorise fully: 12x2 + 20x

Answer: 4x(3x + 5)

  1. Highest common factor: 4x
  2. 12x2 + 20x = 4x(3x + 5)
  3. Check by expanding the brackets.
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