Factorisation of an algebraic expression is the reverse process of expanding.
It involves placing brackets into an expression.
A sum of terms then becomes a product.
Common Factors
If every term of the expression has a common factor, this common factor can be removed and placed outside a set of brackets.
Expression

Common factor

Factors

6p + 12

6

6(p + 2)

6x + 9y − 12z

3

3(2x + 3y − 4z)

2x − 4

2

2(x + 2)

6xy − 18x

6x

6x(y − 3)

5x^{2} + 10xy 
5x

5x(x + 2y)

Once an expression has been factorised, it should then be expanded to check it is correct.
Some expressions cannot be factorised.