Expanding & Factorising
Expanding and factorising are opposites — one opens brackets, the other packs them up.
Expanding single bracketsExpanding double bracketsFactorisingFactorising quadratics
📖 Learn
Double brackets
(x + 3)(x + 5): multiply every term by every term → x² + 8x + 15.
Factorise
Take out the highest common factor: 6x + 9 = 3(2x + 3).
Quadratics
x² + 7x + 12: find two numbers that multiply to 12 and add to 7 → (x + 3)(x + 4).
Worked example
Expand (x + 2)(x + 6)
- 1x × x = x²
- 2x × 6 + 2 × x = 8x
- 32 × 6 = 12 → x² + 8x + 12 ✅
⭐ Practise
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