Expanding and simplifying

Numbers and variables satisfy an important general property, called the distributive law:

            a(b + c) = ab + ac

We use the distributive law to write expressions such as 3(x + 1) in a form that has no brackets,

3(x + 1) = 3 x x + 3 x 1
            = 3x + 3

We say that we have expanded 3(x + 1) to get 3x + 3.

To expand is to get rid of the brackets.

The distributive law says that:

            a(b + c) = ab + ac

In fact, more than this is true:

            a(b + c + d) = ab + ac + ad

and

            a(b + c + d + e) = ab + ac + ad + ae

and so on.