The problem is to force sympy simplyfing sqrt(x**4+4*x**2+4).
positive=True and factor at the good level work. The problem is that in my knowledge in sympy there is no built-in "apply a function f at all levels", so I used a loop over the levels from a high-enough on (5). I'd like to know if there are more elegant ways to proceed...
x=Symbol("x",positive=True) expr = 16*x**3/(-x**2 + sqrt(8*x**2 + (x**2 - 2)**2) + 2)**2 - 2*2**(S(4)/5
... )*x*(-x**2 + sqrt(8*x**2 + (x**2 - 2)**2) + 2)**(S(3)/5) + 10*x
e=expr for i in range(5,-1,-1): e=use(e,factor,i) e
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