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

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

1.Factorise fully: 45x − 36y

Answer: 9(5x − 4y)

  1. Highest common factor: 9
  2. 45x − 36y = 9(5x − 4y)
  3. Check by expanding the brackets.
2.Factorise fully: 15x2 + 35x

Answer: 5x(3x + 7)

  1. Highest common factor: 5x
  2. 15x2 + 35x = 5x(3x + 7)
  3. Check by expanding the brackets.
3.Factorise fully: 10a − 35b

Answer: 5(2a − 7b)

  1. Highest common factor: 5
  2. 10a − 35b = 5(2a − 7b)
  3. Check by expanding the brackets.
4.Factorise fully: 18x2 − 21x

Answer: 3x(6x − 7)

  1. Highest common factor: 3x
  2. 18x2 − 21x = 3x(6x − 7)
  3. Check by expanding the brackets.
5.Factorise fully: 15m − 35n

Answer: 5(3m − 7n)

  1. Highest common factor: 5
  2. 15m − 35n = 5(3m − 7n)
  3. Check by expanding the brackets.
6.Factorise fully: 20x2 − 5x

Answer: 5x(4x − 1)

  1. Highest common factor: 5x
  2. 20x2 − 5x = 5x(4x − 1)
  3. Check by expanding the brackets.
7.Factorise fully: 10x + 14y

Answer: 2(5x + 7y)

  1. Highest common factor: 2
  2. 10x + 14y = 2(5x + 7y)
  3. Check by expanding the brackets.
8.Factorise fully: 18x2 − 42x

Answer: 6x(3x − 7)

  1. Highest common factor: 6x
  2. 18x2 − 42x = 6x(3x − 7)
  3. Check by expanding the brackets.
9.Factorise fully: 45a − 81b

Answer: 9(5a − 9b)

  1. Highest common factor: 9
  2. 45a − 81b = 9(5a − 9b)
  3. Check by expanding the brackets.
10.Factorise fully: 12x2 − 15x

Answer: 3x(4x − 5)

  1. Highest common factor: 3x
  2. 12x2 − 15x = 3x(4x − 5)
  3. Check by expanding the brackets.
11.Factorise fully: 25m − 40n

Answer: 5(5m − 8n)

  1. Highest common factor: 5
  2. 25m − 40n = 5(5m − 8n)
  3. Check by expanding the brackets.
12.Factorise fully: 8x2 − 20x

Answer: 4x(2x − 5)

  1. Highest common factor: 4x
  2. 8x2 − 20x = 4x(2x − 5)
  3. Check by expanding the brackets.
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