Thanks for responding Aaron. Here is the relevant part of my session for 
the attempted r substitution. Can you tell me what I'm doing incorrectly 
and how to do it right?

In [113]: f = j*(3*x**4 + 6*x**2*y**2 - 24*x**2*z**2 + 3*y**4 - 
24*y**2*z**2 + 8*z**4)/(2*(x**2 + y**2 + z**2)**(9/2))

In [114]: f
Out[114]: j*(x**2 + y**2 + z**2)**(-4.5)*(3*x**4 + 6*x**2*y**2 - 
24*x**2*z**2 + 3*y**4 - 24*y**2*z**2 + 8*z**4)/2

In [115]: f.subs(sympy.sqrt(x**2+y**2+z**2),r)
Out[115]: j*(x**2 + y**2 + z**2)**(-4.5)*(3*x**4 + 6*x**2*y**2 - 
24*x**2*z**2 + 3*y**4 - 24*y**2*z**2 + 8*z**4)/2




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