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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — 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 — Practice Set 3 — Answers

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

1.Factorise fully: 12m + 6n

Answer: 6(2m + n)

  1. Highest common factor: 6
  2. 12m + 6n = 6(2m + n)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 + 7x

Answer: x(6x + 7)

  1. Highest common factor: x
  2. 6x2 + 7x = x(6x + 7)
  3. Check by expanding the brackets.
3.Factorise fully: 20m + 32n

Answer: 4(5m + 8n)

  1. Highest common factor: 4
  2. 20m + 32n = 4(5m + 8n)
  3. Check by expanding the brackets.
4.Factorise fully: 6x2 + 24x

Answer: 6x(x + 4)

  1. Highest common factor: 6x
  2. 6x2 + 24x = 6x(x + 4)
  3. Check by expanding the brackets.
5.Factorise fully: 27a − 18b

Answer: 9(3a − 2b)

  1. Highest common factor: 9
  2. 27a − 18b = 9(3a − 2b)
  3. Check by expanding the brackets.
6.Factorise fully: 2x2 − 2x

Answer: 2x(x − 1)

  1. Highest common factor: 2x
  2. 2x2 − 2x = 2x(x − 1)
  3. Check by expanding the brackets.
7.Factorise fully: 24x − 4y

Answer: 4(6x − y)

  1. Highest common factor: 4
  2. 24x − 4y = 4(6x − y)
  3. Check by expanding the brackets.
8.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.
9.Factorise fully: 18m − 63n

Answer: 9(2m − 7n)

  1. Highest common factor: 9
  2. 18m − 63n = 9(2m − 7n)
  3. Check by expanding the brackets.
10.Factorise fully: 25x2 + 30x

Answer: 5x(5x + 6)

  1. Highest common factor: 5x
  2. 25x2 + 30x = 5x(5x + 6)
  3. Check by expanding the brackets.
11.Factorise fully: 20m + 25n

Answer: 5(4m + 5n)

  1. Highest common factor: 5
  2. 20m + 25n = 5(4m + 5n)
  3. Check by expanding the brackets.
12.Factorise fully: 3x2 + 21x

Answer: 3x(x + 7)

  1. Highest common factor: 3x
  2. 3x2 + 21x = 3x(x + 7)
  3. Check by expanding the brackets.
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