Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 Factorise 3x + 12. (like 3(x+4))
Show worked solution
HCF 3 → 3(x + 4).
2 Factorise 7a − 21. (like 7(a-3))
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HCF 7 → 7(a − 3).
3 What is the HCF of 10m and 15m? (as a simplified expression)
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Numbers: 5; both share m → 5m.
Level 2 · Core
4 Factorise 8y2 + 12y. (like 4y(2y+3))
Show worked solution
HCF 4y: 8y2 ÷ 4y = 2y, 12y ÷ 4y = 3 → 4y(2y + 3).
5 Factorise 6ab + 9b. (like 3b(2a+3))
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HCF 3b → 3b(2a + 3).
6 Use factorising mentally: 36 × 7 + 64 × 7.
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7(36 + 64) = 7 × 100 = 700.
Level 3 · Challenge
7 Factorise −10x − 15. (like -5(2x+3))
Show worked solution
Leading negative → pull out −5: −5(2x + 3).
8 Factorise 6x2 + 4x + 10xy. (like 2x(3x+2+5y))
Show worked solution
HCF 2x across all three terms → 2x(3x + 2 + 5y).
9 Factorise 9a2b − 6ab2. (like 3ab(3a-2b))
Show worked solution
HCF 3ab: 9a2b ÷ 3ab = 3a, −6ab2 ÷ 3ab = −2b → 3ab(3a − 2b).