The simplest expressions to factorise have one common factor and factorise into one bracket.

Example:

has a common factor of 2. We write down 2 first and then fill out the inside of the bracket so that when it is multiplied out, is the result. Therefore,

Sometimes we have expressions with more than one common factor, for example,

This also has a common factor 2, but there is another common factor of Hence is a common factor, and the expression factorises:

The last expression had one variable but sometimes there is more than one. The expression below has variables and as well as a constant factor of 3.

To find the common factors we have to look at the powers. In general the highest common factor has the smallest power.

The highest common factor of and is

The highest common factor of and is

So the highest common factor of and is

Hence

Any number can be a constant factor, even a fraction, even if the factor is less than one.

In this example is a factor.

When the denominators are not the same, we add the terms as fractions first.

Now we can factorise with to give