Comment #3 on issue 1498 by [email protected]: Implement symbolic lcm,  
gcd
http://code.google.com/p/sympy/issues/detail?id=1498

I think what you are looking for is this:

In [20]: gcd(y*(1+x)**2, (1-x**2)*y,x,y)
Out[20]: y + x⋅y

It's not very well documented, but it's there.

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