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: 54a − 63b

Answer: 9(6a − 7b)

  1. Highest common factor: 9
  2. 54a − 63b = 9(6a − 7b)
  3. Check by expanding the brackets.
2.Factorise fully: 20x2 + 16x

Answer: 4x(5x + 4)

  1. Highest common factor: 4x
  2. 20x2 + 16x = 4x(5x + 4)
  3. Check by expanding the brackets.
3.Factorise fully: 15a − 40b

Answer: 5(3a − 8b)

  1. Highest common factor: 5
  2. 15a − 40b = 5(3a − 8b)
  3. Check by expanding the brackets.
4.Factorise fully: 10x2 − 12x

Answer: 2x(5x − 6)

  1. Highest common factor: 2x
  2. 10x2 − 12x = 2x(5x − 6)
  3. Check by expanding the brackets.
5.Factorise fully: 8m + 18n

Answer: 2(4m + 9n)

  1. Highest common factor: 2
  2. 8m + 18n = 2(4m + 9n)
  3. Check by expanding the brackets.
6.Factorise fully: 4x2 − 24x

Answer: 4x(x − 6)

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

Answer: 2(5x − 2y)

  1. Highest common factor: 2
  2. 10x − 4y = 2(5x − 2y)
  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: 40x + 56y

Answer: 8(5x + 7y)

  1. Highest common factor: 8
  2. 40x + 56y = 8(5x + 7y)
  3. Check by expanding the brackets.
10.Factorise fully: 18x2 − 15x

Answer: 3x(6x − 5)

  1. Highest common factor: 3x
  2. 18x2 − 15x = 3x(6x − 5)
  3. Check by expanding the brackets.
11.Factorise fully: 20m + 28n

Answer: 4(5m + 7n)

  1. Highest common factor: 4
  2. 20m + 28n = 4(5m + 7n)
  3. Check by expanding the brackets.
12.Factorise fully: 3x2 + 8x

Answer: x(3x + 8)

  1. Highest common factor: x
  2. 3x2 + 8x = x(3x + 8)
  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: