Success TutoringWorksheets

Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 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 + 24b

Answer: 6(3a + 4b)

  1. Highest common factor: 6
  2. 18a + 24b = 6(3a + 4b)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 + 4x

Answer: 4x(x + 1)

  1. Highest common factor: 4x
  2. 4x2 + 4x = 4x(x + 1)
  3. Check by expanding the brackets.
3.Factorise fully: 18m + 15n

Answer: 3(6m + 5n)

  1. Highest common factor: 3
  2. 18m + 15n = 3(6m + 5n)
  3. Check by expanding the brackets.
4.Factorise fully: 15x2 − 27x

Answer: 3x(5x − 9)

  1. Highest common factor: 3x
  2. 15x2 − 27x = 3x(5x − 9)
  3. Check by expanding the brackets.
5.Factorise fully: 25a + 35b

Answer: 5(5a + 7b)

  1. Highest common factor: 5
  2. 25a + 35b = 5(5a + 7b)
  3. Check by expanding the brackets.
6.Factorise fully: 4x2 + 5x

Answer: x(4x + 5)

  1. Highest common factor: x
  2. 4x2 + 5x = x(4x + 5)
  3. Check by expanding the brackets.
7.Factorise fully: 27x + 9y

Answer: 9(3x + y)

  1. Highest common factor: 9
  2. 27x + 9y = 9(3x + y)
  3. Check by expanding the brackets.
8.Factorise fully: x2 − 8x

Answer: x(x − 8)

  1. Highest common factor: x
  2. x2 − 8x = x(x − 8)
  3. Check by expanding the brackets.
9.Factorise fully: 6m − 21n

Answer: 3(2m − 7n)

  1. Highest common factor: 3
  2. 6m − 21n = 3(2m − 7n)
  3. Check by expanding the brackets.
10.Factorise fully: 6x2 + 18x

Answer: 6x(x + 3)

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

Answer: 6(x + 2y)

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

Answer: 3x(2x + 9)

  1. Highest common factor: 3x
  2. 6x2 + 27x = 3x(2x + 9)
  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: