# 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

= 3

*+ 3*

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

*+ 3.*

*x*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.