Success TutoringWorksheets

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.

Download answers PDFPrint answersBack to worksheet
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: 45m − 27n

Answer: 9(5m − 3n)

  1. Highest common factor: 9
  2. 45m − 27n = 9(5m − 3n)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 − 14x

Answer: 2x(2x − 7)

  1. Highest common factor: 2x
  2. 4x2 − 14x = 2x(2x − 7)
  3. Check by expanding the brackets.
3.Factorise fully: 9m − 3n

Answer: 3(3m − n)

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

Answer: x(5x + 4)

  1. Highest common factor: x
  2. 5x2 + 4x = x(5x + 4)
  3. Check by expanding the brackets.
5.Factorise fully: 36x + 6y

Answer: 6(6x + y)

  1. Highest common factor: 6
  2. 36x + 6y = 6(6x + y)
  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: 25x − 45y

Answer: 5(5x − 9y)

  1. Highest common factor: 5
  2. 25x − 45y = 5(5x − 9y)
  3. Check by expanding the brackets.
8.Factorise fully: 15x2 + 10x

Answer: 5x(3x + 2)

  1. Highest common factor: 5x
  2. 15x2 + 10x = 5x(3x + 2)
  3. Check by expanding the brackets.
9.Factorise fully: 36a + 6b

Answer: 6(6a + b)

  1. Highest common factor: 6
  2. 36a + 6b = 6(6a + b)
  3. Check by expanding the brackets.
10.Factorise fully: 2x2 − x

Answer: x(2x − 1)

  1. Highest common factor: x
  2. 2x2 − x = x(2x − 1)
  3. Check by expanding the brackets.
11.Factorise fully: 35a − 56b

Answer: 7(5a − 8b)

  1. Highest common factor: 7
  2. 35a − 56b = 7(5a − 8b)
  3. Check by expanding the brackets.
12.Factorise fully: 25x2 + 30x

Answer: 5x(5x + 6)

  1. Highest common factor: 5x
  2. 25x2 + 30x = 5x(5x + 6)
  3. Check by expanding the brackets.
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: