Success TutoringWorksheets

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

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

1.Factorise fully: −10x − 35

Answer: −5(2x + 7)

  1. Highest common factor: −5
  2. −10x − 35 = −5(2x + 7)
  3. Check by expanding the brackets.
2.Factorise fully: 2x2 − 14x − 10

Answer: 2(x2−7x−5)

  1. Highest common factor: 2
  2. 2x2 − 14x − 10 = 2(x2 − 7x − 5)
  3. Check by expanding the brackets.
3.Factorise fully: 15ab − 25a

Answer: 5a(3b − 5)

  1. Highest common factor: 5a
  2. 15ab − 25a = 5a(3b − 5)
  3. Check by expanding the brackets.
4.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.
5.Factorise fully: 15x2 − 35x − 15

Answer: 5(3x2−7x−3)

  1. Highest common factor: 5
  2. 15x2 − 35x − 15 = 5(3x2 − 7x − 3)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 18a

Answer: 6a(2b − 3)

  1. Highest common factor: 6a
  2. 12ab − 18a = 6a(2b − 3)
  3. Check by expanding the brackets.
7.Factorise fully: −6x + 10

Answer: −2(3x − 5)

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

Answer: 2(x2−4x+9)

  1. Highest common factor: 2
  2. 2x2 − 8x + 18 = 2(x2 − 4x + 9)
  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: −15x − 18

Answer: −3(5x + 6)

  1. Highest common factor: −3
  2. −15x − 18 = −3(5x + 6)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 − 10x − 16

Answer: 2(3x2−5x−8)

  1. Highest common factor: 2
  2. 6x2 − 10x − 16 = 2(3x2 − 5x − 8)
  3. Check by expanding the brackets.
12.Factorise fully: 20ab − 5a

Answer: 5a(4b − 1)

  1. Highest common factor: 5a
  2. 20ab − 5a = 5a(4b − 1)
  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: