There are a number of Maple functions which allow use to manipulate expressions in various ways. They are mostly used for polynomials in the dependent expression, but can sometimes be used in more complicated situations.

These functions generally expect an expression as their first argument, since they need to know the name of the free variable. Thus we would call simplify(f(x),x); rather than simplify(f,x). Most of these functions have the syntax function(expression, variable name[, optional arguments]). Many of these functions only find thier real power when dealing with multivariate functions, though some of them are useful for functions of one variable.

Function	Syntax	Explanation
expand	expand(expression)	Distributes sums across products and applies certain algebraic rules
combine	combine(expression)	Combines varibles in an expression using algebraic rules (opposite of expand).
simplify	simplify(expression)	Simplifies an expression as much as possible.

Notes

When using these functions it is important to realise the mathematical limitations implicit in them.
You are encouraged to use the Maple online help for these functions.

Combine and Expand

Expand allows further expression as optional arguments which indicate that this expression should not be expanded. Some examples:
>expand(x*(x+1)*(x+2));
>expand(x*(x+1)*(x+2), x+1);
>expand(sin(x)*(x+cos(x)));
>expand(sin(a+b)*(a+cos(a+b)));
>expand(sin(a+b)*(a+cos(a+b)), sin(a+b));
>expand(sin(a+b)*(a+cos(a+b)), sin(a+b), cos(a+b));

Simplify

Another optional argument uses the 'assume property' syntax. Thus we may tell Maple that the variables are assumed to have some special property.
The syntax is simplify(expression, assume=property), where property is one of
positive, real, integer, a range (as with the piecewise function)
There are other properties, see help on assume.
Consider the following example:
> g:=sqrt(x^2);

Factor