Maths Help UK

Factorising into a single bracket

Spot the highest common factor, take it outside the bracket. Reverse of expanding.

Look for the largest factor (number, letter, or both) common to every term. Take it outside; what's left goes inside the bracket.

Worked examples
6x + 9 = 3(2x + 3). HCF = 3.
x² + 5x = x(x + 5). HCF = x.
12a²b − 8ab² = 4ab(3a − 2b). HCF = 4ab.

Frequently asked questions

How to check?
Expand the bracket again — you should get the original expression.
Could I take 2 instead of 3 in 6x+9?
Yes but it's not fully factorised. The aim is the highest common factor.