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 :

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

Collect the powers of :

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

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

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

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

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

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

In[6]:=
Click for copyable input
Out[6]=

Get the coefficient of (the constant term):

In[7]:=
Click for copyable input
Out[7]=

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

In[8]:=
Click for copyable input
Out[8]=

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

In[9]:=
Click for copyable input
Out[9]=

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

In[10]:=
Click for copyable input
Out[10]//TraditionalForm=
New to Mathematica? Find your learning path »
Have a question? Ask support »