This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
How to | Rearrange the Terms of a Polynomial
Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary expression structures.
Define a polynomial in and exponentials of :
 Out[2]=
Collect the powers of :
 Out[3]=
Group terms that match the pattern; in this case terms that have the same exponential factors are grouped:
 Out[4]=
Apply Simplify to the coefficient of each term after collecting the terms:
 Out[5]=

There are many ways to extract terms from an expression. Here is a polynomial in :
 Out[6]=
Get the coefficient of (the constant term):
 Out[7]=
Get the same term by replacing with zero, thus eliminating all terms that depend on :
 Out[8]=
Get the list of the monomials ordered from high to low powers of :
 Out[9]=
The polynomial will appear in the same order when displayed in TraditionalForm: