Success TutoringWorksheets

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

Take out the highest common factor. Where the first term is negative, take out a negative factor.

1.Factorise fully: −40x − 16

Answer: −8(5x + 2)

  1. Highest common factor: −8
  2. −40x − 16 = −8(5x + 2)
  3. Check by expanding the brackets.
2.Factorise fully: 9x2 + 9x + 24

Answer: 3(3x2+3x+8)

  1. Highest common factor: 3
  2. 9x2 + 9x + 24 = 3(3x2 + 3x + 8)
  3. Check by expanding the brackets.
3.Factorise fully: 24ab + 6a

Answer: 6a(4b + 1)

  1. Highest common factor: 6a
  2. 24ab + 6a = 6a(4b + 1)
  3. Check by expanding the brackets.
4.Factorise fully: −4x − 20

Answer: −4(x + 5)

  1. Highest common factor: −4
  2. −4x − 20 = −4(x + 5)
  3. Check by expanding the brackets.
5.Factorise fully: 15x2 − 35x − 40

Answer: 5(3x2−7x−8)

  1. Highest common factor: 5
  2. 15x2 − 35x − 40 = 5(3x2 − 7x − 8)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 16a

Answer: 4a(3b − 4)

  1. Highest common factor: 4a
  2. 12ab − 16a = 4a(3b − 4)
  3. Check by expanding the brackets.
7.Factorise fully: −24x − 42

Answer: −6(4x + 7)

  1. Highest common factor: −6
  2. −24x − 42 = −6(4x + 7)
  3. Check by expanding the brackets.
8.Factorise fully: 24x2 − 30x + 12

Answer: 6(4x2−5x+2)

  1. Highest common factor: 6
  2. 24x2 − 30x + 12 = 6(4x2 − 5x + 2)
  3. Check by expanding the brackets.
9.Factorise fully: 2ab + 14a

Answer: 2a(b + 7)

  1. Highest common factor: 2a
  2. 2ab + 14a = 2a(b + 7)
  3. Check by expanding the brackets.
10.Factorise fully: −12x − 32

Answer: −4(3x + 8)

  1. Highest common factor: −4
  2. −12x − 32 = −4(3x + 8)
  3. Check by expanding the brackets.
11.Factorise fully: 4x2 − 20x − 8

Answer: 4(x2−5x−2)

  1. Highest common factor: 4
  2. 4x2 − 20x − 8 = 4(x2 − 5x − 2)
  3. Check by expanding the brackets.
12.Factorise fully: 5ab − 30a

Answer: 5a(b − 6)

  1. Highest common factor: 5a
  2. 5ab − 30a = 5a(b − 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: