Year 10 Factorising Expressions (Common Factors) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 algebraic expressions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Algebraic ExpressionsYear 10 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: 45x + 63
Answer: 9(5x + 7)
- Highest common factor: 9
- 45x + 63 = 9(5x + 7)
- Check by expanding the brackets.
2.Factorise fully: 36x − 45
Answer: 9(4x − 5)
- Highest common factor: 9
- 36x − 45 = 9(4x − 5)
- Check by expanding the brackets.
3.Factorise fully: 27x − 18
Answer: 9(3x − 2)
- Highest common factor: 9
- 27x − 18 = 9(3x − 2)
- 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: 24x − 64
Answer: 8(3x − 8)
- Highest common factor: 8
- 24x − 64 = 8(3x − 8)
- Check by expanding the brackets.
6.Factorise fully: 12x + 10
Answer: 2(6x + 5)
- Highest common factor: 2
- 12x + 10 = 2(6x + 5)
- Check by expanding the brackets.
7.Factorise fully: 28x + 49
Answer: 7(4x + 7)
- Highest common factor: 7
- 28x + 49 = 7(4x + 7)
- Check by expanding the brackets.
8.Factorise fully: 45x + 54
Answer: 9(5x + 6)
- Highest common factor: 9
- 45x + 54 = 9(5x + 6)
- Check by expanding the brackets.
9.Factorise fully: 48x − 8
Answer: 8(6x − 1)
- Highest common factor: 8
- 48x − 8 = 8(6x − 1)
- Check by expanding the brackets.
10.Factorise fully: 14x − 21
Answer: 7(2x − 3)
- Highest common factor: 7
- 14x − 21 = 7(2x − 3)
- Check by expanding the brackets.
11.Factorise fully: 14x − 63
Answer: 7(2x − 9)
- Highest common factor: 7
- 14x − 63 = 7(2x − 9)
- Check by expanding the brackets.
12.Factorise fully: 8x − 56
Answer: 8(x − 7)
- Highest common factor: 8
- 8x − 56 = 8(x − 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.