simplification of (4-4*x^2)*sqrt(1-x^2)



Barton Willis wrote:
> Automatically, we have (1-x^2) * sqrt(1-x^2) --> (1-x^2)^(3/2), but I don't
> even
> know of a command that crunches (4-4*x^2)*sqrt(1-x^2) --> 4 * (1-x^2)^
> (3/2). Is there
> a command that does this simplification?
>   

not exactly automatic:

tellrat(1-x^2=y);
algebraic:true;

rat( (4-4*x^2)*y)   -->  4 * y^3.