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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 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: 15x + 25y

Answer: 5(3x + 5y)

  1. Highest common factor: 5
  2. 15x + 25y = 5(3x + 5y)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 − 6x

Answer: 2x(2x − 3)

  1. Highest common factor: 2x
  2. 4x2 − 6x = 2x(2x − 3)
  3. Check by expanding the brackets.
3.Factorise fully: 25a + 35b

Answer: 5(5a + 7b)

  1. Highest common factor: 5
  2. 25a + 35b = 5(5a + 7b)
  3. Check by expanding the brackets.
4.Factorise fully: 20x2 + 28x

Answer: 4x(5x + 7)

  1. Highest common factor: 4x
  2. 20x2 + 28x = 4x(5x + 7)
  3. Check by expanding the brackets.
5.Factorise fully: 15m − 24n

Answer: 3(5m − 8n)

  1. Highest common factor: 3
  2. 15m − 24n = 3(5m − 8n)
  3. Check by expanding the brackets.
6.Factorise fully: 6x2 + x

Answer: x(6x + 1)

  1. Highest common factor: x
  2. 6x2 + x = x(6x + 1)
  3. Check by expanding the brackets.
7.Factorise fully: 30a + 36b

Answer: 6(5a + 6b)

  1. Highest common factor: 6
  2. 30a + 36b = 6(5a + 6b)
  3. Check by expanding the brackets.
8.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.
9.Factorise fully: 28x − 49y

Answer: 7(4x − 7y)

  1. Highest common factor: 7
  2. 28x − 49y = 7(4x − 7y)
  3. Check by expanding the brackets.
10.Factorise fully: 10x2 − 35x

Answer: 5x(2x − 7)

  1. Highest common factor: 5x
  2. 10x2 − 35x = 5x(2x − 7)
  3. Check by expanding the brackets.
11.Factorise fully: 10a + 5b

Answer: 5(2a + b)

  1. Highest common factor: 5
  2. 10a + 5b = 5(2a + b)
  3. Check by expanding the brackets.
12.Factorise fully: 18x2 − 48x

Answer: 6x(3x − 8)

  1. Highest common factor: 6x
  2. 18x2 − 48x = 6x(3x − 8)
  3. Check by expanding the brackets.
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