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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: 45a − 63b

Answer: 9(5a − 7b)

  1. Highest common factor: 9
  2. 45a − 63b = 9(5a − 7b)
  3. Check by expanding the brackets.
2.Factorise fully: 24x2 + 4x

Answer: 4x(6x + 1)

  1. Highest common factor: 4x
  2. 24x2 + 4x = 4x(6x + 1)
  3. Check by expanding the brackets.
3.Factorise fully: 4x + 10y

Answer: 2(2x + 5y)

  1. Highest common factor: 2
  2. 4x + 10y = 2(2x + 5y)
  3. Check by expanding the brackets.
4.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.
5.Factorise fully: 36m − 30n

Answer: 6(6m − 5n)

  1. Highest common factor: 6
  2. 36m − 30n = 6(6m − 5n)
  3. Check by expanding the brackets.
6.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.
7.Factorise fully: 45x + 81y

Answer: 9(5x + 9y)

  1. Highest common factor: 9
  2. 45x + 81y = 9(5x + 9y)
  3. Check by expanding the brackets.
8.Factorise fully: x2 + 4x

Answer: x(x + 4)

  1. Highest common factor: x
  2. x2 + 4x = x(x + 4)
  3. Check by expanding the brackets.
9.Factorise fully: 8m − 56n

Answer: 8(m − 7n)

  1. Highest common factor: 8
  2. 8m − 56n = 8(m − 7n)
  3. Check by expanding the brackets.
10.Factorise fully: 15x2 − 6x

Answer: 3x(5x − 2)

  1. Highest common factor: 3x
  2. 15x2 − 6x = 3x(5x − 2)
  3. Check by expanding the brackets.
11.Factorise fully: 4a − 12b

Answer: 4(a − 3b)

  1. Highest common factor: 4
  2. 4a − 12b = 4(a − 3b)
  3. Check by expanding the brackets.
12.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.
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