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Unexpected non-evaluation problem


I am totally baffled by the following Mathematica behavior:

  In[1]:= InverseFourierTransform[FourierTransform[x^2, x, y], y, x]
  Out[1]= Sqrt[2 Pi] x^2 FourierTransform[DiracDelta[y], y, x]

  In[2]:= Sqrt[2 Pi] x^2 FourierTransform[DiracDelta[y], y, x]
  Out[2]= x^2

I've already asked my local guru without success, so I'm hoping someone
here can help me. Does anyone know why the first expression doesn't
evaluate to x^2 all by itself? How I can force it to do so?

Carl


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