Year 8 Factorising Expressions (Common Factors) Worksheet — Level 1 — Practice Set 4 — 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 — Practice Set 4 — Answers
Find the highest common factor of the terms and write it outside the brackets.
1.Factorise fully: 6x − 30
Answer: 6(x − 5)
- Highest common factor: 6
- 6x − 30 = 6(x − 5)
- Check by expanding the brackets.
2.Factorise fully: 4x − 36
Answer: 4(x − 9)
- Highest common factor: 4
- 4x − 36 = 4(x − 9)
- Check by expanding the brackets.
3.Factorise fully: 6x + 15
Answer: 3(2x + 5)
- Highest common factor: 3
- 6x + 15 = 3(2x + 5)
- Check by expanding the brackets.
4.Factorise fully: 8x + 32
Answer: 8(x + 4)
- Highest common factor: 8
- 8x + 32 = 8(x + 4)
- Check by expanding the brackets.
5.Factorise fully: 15x + 18
Answer: 3(5x + 6)
- Highest common factor: 3
- 15x + 18 = 3(5x + 6)
- Check by expanding the brackets.
6.Factorise fully: 54x − 45
Answer: 9(6x − 5)
- Highest common factor: 9
- 54x − 45 = 9(6x − 5)
- Check by expanding the brackets.
7.Factorise fully: 15x − 18
Answer: 3(5x − 6)
- Highest common factor: 3
- 15x − 18 = 3(5x − 6)
- Check by expanding the brackets.
8.Factorise fully: 30x + 18
Answer: 6(5x + 3)
- Highest common factor: 6
- 30x + 18 = 6(5x + 3)
- Check by expanding the brackets.
9.Factorise fully: 40x + 32
Answer: 8(5x + 4)
- Highest common factor: 8
- 40x + 32 = 8(5x + 4)
- Check by expanding the brackets.
10.Factorise fully: 25x − 45
Answer: 5(5x − 9)
- Highest common factor: 5
- 25x − 45 = 5(5x − 9)
- Check by expanding the brackets.
11.Factorise fully: 15x − 5
Answer: 5(3x − 1)
- Highest common factor: 5
- 15x − 5 = 5(3x − 1)
- Check by expanding the brackets.
12.Factorise fully: 6x + 14
Answer: 2(3x + 7)
- Highest common factor: 2
- 6x + 14 = 2(3x + 7)
- 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.