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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers

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

1.Factorise fully: 12a + 2b

Answer: 2(6a + b)

  1. Highest common factor: 2
  2. 12a + 2b = 2(6a + b)
  3. Check by expanding the brackets.
2.Factorise fully: 3x2 + 18x

Answer: 3x(x + 6)

  1. Highest common factor: 3x
  2. 3x2 + 18x = 3x(x + 6)
  3. Check by expanding the brackets.
3.Factorise fully: 25m + 10n

Answer: 5(5m + 2n)

  1. Highest common factor: 5
  2. 25m + 10n = 5(5m + 2n)
  3. Check by expanding the brackets.
4.Factorise fully: 20x2 + 45x

Answer: 5x(4x + 9)

  1. Highest common factor: 5x
  2. 20x2 + 45x = 5x(4x + 9)
  3. Check by expanding the brackets.
5.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.
6.Factorise fully: 24x2 − 42x

Answer: 6x(4x − 7)

  1. Highest common factor: 6x
  2. 24x2 − 42x = 6x(4x − 7)
  3. Check by expanding the brackets.
7.Factorise fully: 18m + 30n

Answer: 6(3m + 5n)

  1. Highest common factor: 6
  2. 18m + 30n = 6(3m + 5n)
  3. Check by expanding the brackets.
8.Factorise fully: 12x2 + 27x

Answer: 3x(4x + 9)

  1. Highest common factor: 3x
  2. 12x2 + 27x = 3x(4x + 9)
  3. Check by expanding the brackets.
9.Factorise fully: 2x − 6y

Answer: 2(x − 3y)

  1. Highest common factor: 2
  2. 2x − 6y = 2(x − 3y)
  3. Check by expanding the brackets.
10.Factorise fully: 12x2 − 32x

Answer: 4x(3x − 8)

  1. Highest common factor: 4x
  2. 12x2 − 32x = 4x(3x − 8)
  3. Check by expanding the brackets.
11.Factorise fully: 18a + 9b

Answer: 9(2a + b)

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

Answer: x(2x + 3)

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