How to | Rearrange the Terms of a Polynomial

The Wolfram Language 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 :

In[1]:=
Click for copyable input
Out[1]=

Collect the powers of :

In[2]:=
Click for copyable input
Out[2]=

Group terms that match the pattern; in this case terms that have the same exponential factors are grouped:

In[3]:=
Click for copyable input
Out[3]=

Apply Simplify to the coefficient of each term after collecting the terms:

In[4]:=
Click for copyable input
Out[4]=
    

There are many ways to extract terms from an expression. Here is a polynomial in :

In[1]:=
Click for copyable input
Out[1]=

Get the coefficient of (the constant term):

In[2]:=
Click for copyable input
Out[2]=

Get the same term by replacing with zero, thus eliminating all terms that depend on :

In[3]:=
Click for copyable input
Out[3]=

Get the list of the monomials ordered from high to low powers of :

In[4]:=
Click for copyable input
Out[4]=

The polynomial will appear in the same order when displayed in TraditionalForm:

In[5]:=
Click for copyable input
Out[5]//TraditionalForm=