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

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

1.Factorise fully: 6a − 14b

Answer: 2(3a − 7b)

  1. Highest common factor: 2
  2. 6a − 14b = 2(3a − 7b)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 + 7x

Answer: x(4x + 7)

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

Answer: 6(m − 7n)

  1. Highest common factor: 6
  2. 6m − 42n = 6(m − 7n)
  3. Check by expanding the brackets.
4.Factorise fully: 6x2 − 15x

Answer: 3x(2x − 5)

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

Answer: 3(3m + 2n)

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

Answer: 6x(5x + 1)

  1. Highest common factor: 6x
  2. 30x2 + 6x = 6x(5x + 1)
  3. Check by expanding the brackets.
7.Factorise fully: 6a + 10b

Answer: 2(3a + 5b)

  1. Highest common factor: 2
  2. 6a + 10b = 2(3a + 5b)
  3. Check by expanding the brackets.
8.Factorise fully: 12x2 + 2x

Answer: 2x(6x + 1)

  1. Highest common factor: 2x
  2. 12x2 + 2x = 2x(6x + 1)
  3. Check by expanding the brackets.
9.Factorise fully: 45a − 54b

Answer: 9(5a − 6b)

  1. Highest common factor: 9
  2. 45a − 54b = 9(5a − 6b)
  3. Check by expanding the brackets.
10.Factorise fully: 5x2 − x

Answer: x(5x − 1)

  1. Highest common factor: x
  2. 5x2 − x = x(5x − 1)
  3. Check by expanding the brackets.
11.Factorise fully: 28x + 21y

Answer: 7(4x + 3y)

  1. Highest common factor: 7
  2. 28x + 21y = 7(4x + 3y)
  3. Check by expanding the brackets.
12.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.
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