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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: 18a + 27b

Answer: 9(2a + 3b)

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

Answer: 3x(x − 3)

  1. Highest common factor: 3x
  2. 3x2 − 9x = 3x(x − 3)
  3. Check by expanding the brackets.
3.Factorise fully: 21a + 35b

Answer: 7(3a + 5b)

  1. Highest common factor: 7
  2. 21a + 35b = 7(3a + 5b)
  3. Check by expanding the brackets.
4.Factorise fully: 10x2 − 15x

Answer: 5x(2x − 3)

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

Answer: 7(5a − b)

  1. Highest common factor: 7
  2. 35a − 7b = 7(5a − b)
  3. Check by expanding the brackets.
6.Factorise fully: 10x2 − 25x

Answer: 5x(2x − 5)

  1. Highest common factor: 5x
  2. 10x2 − 25x = 5x(2x − 5)
  3. Check by expanding the brackets.
7.Factorise fully: 12a − 27b

Answer: 3(4a − 9b)

  1. Highest common factor: 3
  2. 12a − 27b = 3(4a − 9b)
  3. Check by expanding the brackets.
8.Factorise fully: 24x2 + 18x

Answer: 6x(4x + 3)

  1. Highest common factor: 6x
  2. 24x2 + 18x = 6x(4x + 3)
  3. Check by expanding the brackets.
9.Factorise fully: 25m − 5n

Answer: 5(5m − n)

  1. Highest common factor: 5
  2. 25m − 5n = 5(5m − n)
  3. Check by expanding the brackets.
10.Factorise fully: 9x2 − 24x

Answer: 3x(3x − 8)

  1. Highest common factor: 3x
  2. 9x2 − 24x = 3x(3x − 8)
  3. Check by expanding the brackets.
11.Factorise fully: 25m + 30n

Answer: 5(5m + 6n)

  1. Highest common factor: 5
  2. 25m + 30n = 5(5m + 6n)
  3. Check by expanding the brackets.
12.Factorise fully: 5x2 + 7x

Answer: x(5x + 7)

  1. Highest common factor: x
  2. 5x2 + 7x = x(5x + 7)
  3. Check by expanding the brackets.
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