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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: 8x − 48y

Answer: 8(x − 6y)

  1. Highest common factor: 8
  2. 8x − 48y = 8(x − 6y)
  3. Check by expanding the brackets.
2.Factorise fully: 30x2 − 48x

Answer: 6x(5x − 8)

  1. Highest common factor: 6x
  2. 30x2 − 48x = 6x(5x − 8)
  3. Check by expanding the brackets.
3.Factorise fully: 8x − 28y

Answer: 4(2x − 7y)

  1. Highest common factor: 4
  2. 8x − 28y = 4(2x − 7y)
  3. Check by expanding the brackets.
4.Factorise fully: 6x2 − 2x

Answer: 2x(3x − 1)

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

Answer: 2(4m − n)

  1. Highest common factor: 2
  2. 8m − 2n = 2(4m − n)
  3. Check by expanding the brackets.
6.Factorise fully: 16x2 − 4x

Answer: 4x(4x − 1)

  1. Highest common factor: 4x
  2. 16x2 − 4x = 4x(4x − 1)
  3. Check by expanding the brackets.
7.Factorise fully: 21x + 49y

Answer: 7(3x + 7y)

  1. Highest common factor: 7
  2. 21x + 49y = 7(3x + 7y)
  3. Check by expanding the brackets.
8.Factorise fully: 4x2 − 2x

Answer: 2x(2x − 1)

  1. Highest common factor: 2x
  2. 4x2 − 2x = 2x(2x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 8x − 12y

Answer: 4(2x − 3y)

  1. Highest common factor: 4
  2. 8x − 12y = 4(2x − 3y)
  3. Check by expanding the brackets.
10.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.
11.Factorise fully: 10m + 45n

Answer: 5(2m + 9n)

  1. Highest common factor: 5
  2. 10m + 45n = 5(2m + 9n)
  3. Check by expanding the brackets.
12.Factorise fully: 30x2 + 12x

Answer: 6x(5x + 2)

  1. Highest common factor: 6x
  2. 30x2 + 12x = 6x(5x + 2)
  3. Check by expanding the brackets.
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