Mathematica 6.0 for Linux x86 (32-bit)
Copyright 1988-2008 Wolfram Research, Inc.

In[1]:= 
Out[1]= 1 - V12 - V13 + V12 V13 - V23 + V12 V23 + V13 V23 - V12 V13 V23

In[2]:= 
In[2]:= 
In[3]:= 
In[3]:= 
                      2                2                2
                   V12              V13              V23
Out[3]= (1 - V12 + ----) (1 - V13 + ----) (1 - V23 + ----)
                    2                2                2

In[4]:= 
In[4]:= 
Out[4]//TeXForm= 
   \text{V13} \text{V12}-\text{V13} \text{V23} \text{V12}+\text{V23}
    \text{V12}-\text{V12}-\text{V13}+\text{V13} \text{V23}-\text{V23}+1

In[5]:= 
Out[5]//TeXForm= 
   \left(\frac{\text{V12}^2}{2}-\text{V12}+1\right)
    \left(\frac{\text{V13}^2}{2}-\text{V13}+1\right)
    \left(\frac{\text{V23}^2}{2}-\text{V23}+1\right)

In[6]:= 
In[6]:= Expand:

In[7]:= 
                     2                      2          2          2
                  V12                    V12  V13   V13    V12 V13
Out[7]= 1 - V12 + ---- - V13 + V12 V13 - -------- + ---- - -------- + 
                   2                        2        2        2
 
        2    2                      2
     V12  V13                    V12  V23
>    --------- - V23 + V12 V23 - -------- + V13 V23 - V12 V13 V23 + 
         4                          2
 
        2              2              2          2    2          2
     V12  V13 V23   V13  V23   V12 V13  V23   V12  V13  V23   V23
>    ------------ - -------- + ------------ - ------------- + ---- - 
          2            2            2               4          2
 
            2      2    2          2              2      2        2
     V12 V23    V12  V23    V13 V23    V12 V13 V23    V12  V13 V23
>    -------- + --------- - -------- + ------------ - ------------- + 
        2           4          2            2               4
 
        2    2          2    2      2    2    2
     V13  V23    V12 V13  V23    V12  V13  V23
>    --------- - ------------- + --------------
         4             4               8

In[8]:= 
Out[8]//TeXForm= 
   \frac{\text{V13}^2 \text{V12}^2}{4}+\frac{1}{8} \text{V13}^2 \text{V23}^2
    \text{V12}^2-\frac{1}{4} \text{V13} \text{V23}^2
    \text{V12}^2+\frac{\text{V23}^2 \text{V12}^2}{4}-\frac{\text{V13}
    \text{V12}^2}{2}-\frac{1}{4} \text{V13}^2 \text{V23}
    \text{V12}^2+\frac{1}{2} \text{V13} \text{V23}
    \text{V12}^2-\frac{\text{V23}
    \text{V12}^2}{2}+\frac{\text{V12}^2}{2}-\frac{\text{V13}^2
    \text{V12}}{2}-\frac{1}{4} \text{V13}^2 \text{V23}^2
    \text{V12}+\frac{1}{2} \text{V13} \text{V23}^2
    \text{V12}-\frac{\text{V23}^2 \text{V12}}{2}+\text{V13}
    \text{V12}+\frac{1}{2} \text{V13}^2 \text{V23} \text{V12}-\text{V13}
    \text{V23} \text{V12}+\text{V23}
    \text{V12}-\text{V12}+\frac{\text{V13}^2}{2}+\frac{\text{V13}^2
    \text{V23}^2}{4}-\frac{\text{V13}
    \text{V23}^2}{2}+\frac{\text{V23}^2}{2}-\text{V13}-\frac{\text{V13}^2
    \text{V23}}{2}+\text{V13} \text{V23}-\text{V23}+1

In[9]:= Simplify:

In[10]:= 
                         2                  2                  2
         (2 - 2 V12 + V12 ) (2 - 2 V13 + V13 ) (2 - 2 V23 + V23 )
Out[10]= --------------------------------------------------------
                                    8

In[11]:=