Any way to define variables as constant?

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So you want to know if a specific mathematical expression (like $(x-1)^2 - (x^2-2x))$ is a constant. Just check whether its derivative is zero:

sage: var('C, C2')
sage: diff(((x-1)^2+C) - (x^2-2*x+C2), x)
0
sage: bool(diff(((x-1)^2+C) - (x^2-2*x+C2), x) == 0)
True

There is no such function, because they're not equal. Perhaps the second expression should be x^2-2x+1+C...

What have you tried? Here are two options:

sage: var('C')
sage: expand(((x-1)^2+C) - (x^2-2*x+1+C))
0
sage: bool(expand((x-1)^2+C) == expand(x^2-2*x+1+C))
True