Year 8 Factorising Expressions (Common Factors) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic ExpressionsYear 8 Factorising Expressions (Common Factors) Worksheet — Level 1 — Answers
Find the highest common factor of the terms and write it outside the brackets.
1.Factorise fully: 21x − 35
Answer: 7(3x − 5)
- Highest common factor: 7
- 21x − 35 = 7(3x − 5)
- Check by expanding the brackets.
2.Factorise fully: 18x − 48
Answer: 6(3x − 8)
- Highest common factor: 6
- 18x − 48 = 6(3x − 8)
- Check by expanding the brackets.
3.Factorise fully: 35x + 28
Answer: 7(5x + 4)
- Highest common factor: 7
- 35x + 28 = 7(5x + 4)
- Check by expanding the brackets.
4.Factorise fully: 27x − 9
Answer: 9(3x − 1)
- Highest common factor: 9
- 27x − 9 = 9(3x − 1)
- Check by expanding the brackets.
5.Factorise fully: 7x + 7
Answer: 7(x + 1)
- Highest common factor: 7
- 7x + 7 = 7(x + 1)
- Check by expanding the brackets.
6.Factorise fully: 20x − 35
Answer: 5(4x − 7)
- Highest common factor: 5
- 20x − 35 = 5(4x − 7)
- Check by expanding the brackets.
7.Factorise fully: 5x − 10
Answer: 5(x − 2)
- Highest common factor: 5
- 5x − 10 = 5(x − 2)
- Check by expanding the brackets.
8.Factorise fully: 8x − 18
Answer: 2(4x − 9)
- Highest common factor: 2
- 8x − 18 = 2(4x − 9)
- Check by expanding the brackets.
9.Factorise fully: 15x − 35
Answer: 5(3x − 7)
- Highest common factor: 5
- 15x − 35 = 5(3x − 7)
- Check by expanding the brackets.
10.Factorise fully: 12x − 14
Answer: 2(6x − 7)
- Highest common factor: 2
- 12x − 14 = 2(6x − 7)
- Check by expanding the brackets.
11.Factorise fully: 6x + 4
Answer: 2(3x + 2)
- Highest common factor: 2
- 6x + 4 = 2(3x + 2)
- Check by expanding the brackets.
12.Factorise fully: 4x − 8
Answer: 4(x − 2)
- Highest common factor: 4
- 4x − 8 = 4(x − 2)
- Check by expanding the brackets.
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.