Year 9 Factorising Expressions (Common Factors) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic ExpressionsYear 9 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: 18x − 6
Answer: 6(3x − 1)
- Highest common factor: 6
- 18x − 6 = 6(3x − 1)
- Check by expanding the brackets.
2.Factorise fully: 35x − 21
Answer: 7(5x − 3)
- Highest common factor: 7
- 35x − 21 = 7(5x − 3)
- Check by expanding the brackets.
3.Factorise fully: 18x − 12
Answer: 6(3x − 2)
- Highest common factor: 6
- 18x − 12 = 6(3x − 2)
- Check by expanding the brackets.
4.Factorise fully: 20x − 35
Answer: 5(4x − 7)
- Highest common factor: 5
- 20x − 35 = 5(4x − 7)
- Check by expanding the brackets.
5.Factorise fully: 35x + 14
Answer: 7(5x + 2)
- Highest common factor: 7
- 35x + 14 = 7(5x + 2)
- Check by expanding the brackets.
6.Factorise fully: 24x − 56
Answer: 8(3x − 7)
- Highest common factor: 8
- 24x − 56 = 8(3x − 7)
- Check by expanding the brackets.
7.Factorise fully: 2x − 4
Answer: 2(x − 2)
- Highest common factor: 2
- 2x − 4 = 2(x − 2)
- Check by expanding the brackets.
8.Factorise fully: 6x + 54
Answer: 6(x + 9)
- Highest common factor: 6
- 6x + 54 = 6(x + 9)
- Check by expanding the brackets.
9.Factorise fully: 15x + 24
Answer: 3(5x + 8)
- Highest common factor: 3
- 15x + 24 = 3(5x + 8)
- Check by expanding the brackets.
10.Factorise fully: 18x − 30
Answer: 6(3x − 5)
- Highest common factor: 6
- 18x − 30 = 6(3x − 5)
- Check by expanding the brackets.
11.Factorise fully: 36x − 27
Answer: 9(4x − 3)
- Highest common factor: 9
- 36x − 27 = 9(4x − 3)
- Check by expanding the brackets.
12.Factorise fully: 18x − 81
Answer: 9(2x − 9)
- Highest common factor: 9
- 18x − 81 = 9(2x − 9)
- 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.