Factorising with Common Factors

Factorising is the reverse of expanding: instead of removing brackets, you put them back. You do this by pulling out the highest common factor (HCF) — the biggest thing that divides every term — and writing it outside a bracket.

Here 3 divides both $6x$ and $9$, so it comes out; what's left inside is what each term becomes after dividing by 3. Variables can be common factors too:

Always check by expanding. Multiply the bracket back out — if you land on the original expression, your factorisation is correct: $2ab(2a - 3b) = 4a^2 b - 6ab^2$ ✓.