How to subtract second level columns in multiIndex level dataframe

Question

Here is the example data I am working with. What I am trying to accomplish is 1) subtract b column from column a and 2) create the C column in front of a and b columns. I would like to loop through and create the C column for x, y and z.

import pandas as pd
df = pd.DataFrame(data=[[100,200,400,500,111,222], [77,28,110,211,27,81], [11,22,33,11,22,33],[213,124,136,147,54,56]])
df.columns = pd.MultiIndex.from_product([['x', 'y', 'z'], list('ab')])
print (df)

Below is what I am trying to get.

Answer 1

Use DataFrame.xs for select second levels with avoid remove first level with drop_level=False, then use rename for same MultiIndex, subtract and add to original with concat, last use DataFrame.sort_index:

dfa = df.xs('a', axis=1, level=1, drop_level=False).rename(columns={'a':'c'})
dfb = df.xs('b', axis=1, level=1, drop_level=False).rename(columns={'b':'c'})

df = pd.concat([df, dfa.sub(dfb)], axis=1).sort_index(axis=1)
print (df)
     x              y              z          
     a    b    c    a    b    c    a    b    c
0  100  200 -100  400  500 -100  111  222 -111
1   77   28   49  110  211 -101   27   81  -54
2   11   22  -11   33   11   22   22   33  -11
3  213  124   89  136  147  -11   54   56   -2

With loop select columns by tuples, subtract Series and last use DataFrame.sort_index:

for c in df.columns.levels[0]:
    df[(c, 'c')] = df[(c, 'a')].sub(df[(c, 'b')])

df = df.sort_index(axis=1)
print (df)
     x              y              z          
     a    b    c    a    b    c    a    b    c
0  100  200 -100  400  500 -100  111  222 -111
1   77   28   49  110  211 -101   27   81  -54
2   11   22  -11   33   11   22   22   33  -11
3  213  124   89  136  147  -11   54   56   -2