Bug in Distribute Function (?)

Questions
1

What’s going on here:
Distribute[(a - b)^2]

Output:a^2 + b^2

While Distribute[(a - b) (c - d)]
gives

a c - b c - a d + b d

Mathematica Version 9.0.1

2

In[2]:= FullForm[(a - b)^2]

Out[2]= Power[Plus[a, Times[-1, b]], 2]

so the square operation is distributed over a and -b inside Plus.

For the desired result, try

In[4]:= Distribute[Unevaluated[(a - b) (a - b)]]

Out[4]= a^2 - 2 a b + b^2

see also ‘Possible Issues’ in the documentation of Distribute.

3

Thank you.
But in future I will use Expand instead of Distribute.

Best regards