Simplification

For the most part, Maple leaves expressions the way you entered them or
the way they were created from some computation.  However, there are
some obvious simplifications that it automatically performs.  An example
of this would be turning 0 * x into the simpler 0.  Other automatic
simplifications are described in the document First Leaves, in the
section "Automatic simplification".

There are two reasons why only a limited number of automatic
simplifications are performed:

* Cost: some simplifications, such as the factoring of expressions, can
be reasonably time-consuming to perform.  The Maple solution to this is
to automatically perform only certain low-cost simplifications, but to
provide ways of forcing more involved methods.

* Preference: different users will consider different styles of
expression as being simpler.  The Maple solution is to provide ways to
specify specific simplification techniques.

The simplify command provides typical expression simplifications.  By
using simplify(expr, variety) you can control what simplifications are
performed:

> (x^y)^z;
  y z
(x )
> simplify((x^y)^z,power);
 (y z)
x

See help('simplify') for the various simplification options.

The expand command forces distribution of multiplication over addition.
For instance:

> f := (x + y) * (x - y);
f := (x + y) (x - y)
> expand(f);
 2    2
x  - y

Since expand turns f into x^2 + y * x - x * y - y^2, the automatic
simplifications turn the expression into x^2 - y^2.

For more information on simplification, see help('simplify'),
help('expand'), help('factor'), help('normal'), and the First Leaves
section on "Simplification of expressions".