Factorising an algebraic expression is the opposite process of expanding brackets.
It involves placing brackets into an expression.
Once an expression has been factorised, it should then be expanded to check it is correct.

Some expressions cannot be factorised.


Common Factors

common factor is a number or letter that divides into each term of an expression.

If every term of the expression has a common factor, this common factor should be taken out and placed in front of a set of brackets.

Unfactorised Expression
Common factor
Other factor
Factorised expression
9p + 12
(3p + 4)
3(3p + 4)
12x − 18y
(2x − 3y)
6(2x − 3y)
4a2 + 8a
(a + 2)
4a(a + 2)