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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers

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

1.Factorise fully: 12x + 30y

Answer: 6(2x + 5y)

  1. Highest common factor: 6
  2. 12x + 30y = 6(2x + 5y)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 + 32x

Answer: 4x(x + 8)

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

Answer: 5(m − n)

  1. Highest common factor: 5
  2. 5m − 5n = 5(m − n)
  3. Check by expanding the brackets.
4.Factorise fully: 15x2 + 21x

Answer: 3x(5x + 7)

  1. Highest common factor: 3x
  2. 15x2 + 21x = 3x(5x + 7)
  3. Check by expanding the brackets.
5.Factorise fully: 8a − 6b

Answer: 2(4a − 3b)

  1. Highest common factor: 2
  2. 8a − 6b = 2(4a − 3b)
  3. Check by expanding the brackets.
6.Factorise fully: 8x2 − 36x

Answer: 4x(2x − 9)

  1. Highest common factor: 4x
  2. 8x2 − 36x = 4x(2x − 9)
  3. Check by expanding the brackets.
7.Factorise fully: 4x + 16y

Answer: 4(x + 4y)

  1. Highest common factor: 4
  2. 4x + 16y = 4(x + 4y)
  3. Check by expanding the brackets.
8.Factorise fully: 30x2 + 5x

Answer: 5x(6x + 1)

  1. Highest common factor: 5x
  2. 30x2 + 5x = 5x(6x + 1)
  3. Check by expanding the brackets.
9.Factorise fully: 6m − 8n

Answer: 2(3m − 4n)

  1. Highest common factor: 2
  2. 6m − 8n = 2(3m − 4n)
  3. Check by expanding the brackets.
10.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.
11.Factorise fully: 21x + 56y

Answer: 7(3x + 8y)

  1. Highest common factor: 7
  2. 21x + 56y = 7(3x + 8y)
  3. Check by expanding the brackets.
12.Factorise fully: 15x2 − 27x

Answer: 3x(5x − 9)

  1. Highest common factor: 3x
  2. 15x2 − 27x = 3x(5x − 9)
  3. Check by expanding the brackets.
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