Year 10 Factorising Expressions (Common Factors) Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Find the highest common factor of the terms and write it outside the brackets.
1.Factorise fully: 35x + 7
Answer: 7(5x + 1)
- Highest common factor: 7
- 35x + 7 = 7(5x + 1)
- Check by expanding the brackets.
2.Factorise fully: 28x − 49
Answer: 7(4x − 7)
- Highest common factor: 7
- 28x − 49 = 7(4x − 7)
- Check by expanding the brackets.
3.Factorise fully: 3x − 27
Answer: 3(x − 9)
- Highest common factor: 3
- 3x − 27 = 3(x − 9)
- Check by expanding the brackets.
4.Factorise fully: 40x − 24
Answer: 8(5x − 3)
- Highest common factor: 8
- 40x − 24 = 8(5x − 3)
- Check by expanding the brackets.
5.Factorise fully: 16x − 40
Answer: 8(2x − 5)
- Highest common factor: 8
- 16x − 40 = 8(2x − 5)
- Check by expanding the brackets.
6.Factorise fully: 9x + 54
Answer: 9(x + 6)
- Highest common factor: 9
- 9x + 54 = 9(x + 6)
- Check by expanding the brackets.
7.Factorise fully: 18x − 48
Answer: 6(3x − 8)
- Highest common factor: 6
- 18x − 48 = 6(3x − 8)
- Check by expanding the brackets.
8.Factorise fully: 12x + 54
Answer: 6(2x + 9)
- Highest common factor: 6
- 12x + 54 = 6(2x + 9)
- Check by expanding the brackets.
9.Factorise fully: 32x − 56
Answer: 8(4x − 7)
- Highest common factor: 8
- 32x − 56 = 8(4x − 7)
- Check by expanding the brackets.
10.Factorise fully: 40x − 8
Answer: 8(5x − 1)
- Highest common factor: 8
- 40x − 8 = 8(5x − 1)
- Check by expanding the brackets.
11.Factorise fully: 12x − 27
Answer: 3(4x − 9)
- Highest common factor: 3
- 12x − 27 = 3(4x − 9)
- Check by expanding the brackets.
12.Factorise fully: 21x + 56
Answer: 7(3x + 8)
- Highest common factor: 7
- 21x + 56 = 7(3x + 8)
- 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.
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