Rearrange function's terms to prove it is nonnegative?

Questions
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1

I added a notebook. I have a function. I know it is non-negative when 1>x>-1 and a,b,c>0.
I want to prove that it is non-negative. I want to rearrange the function so that it can be seen directly that it is non-negative. How can I do that? I can prove it using calculus as well.

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2

Version 13.0 of Mathematica has a new function called PolynomialSumOfSquaresList. I have not tried it yet.

3

Thank you for your answer.
I got an error message. “f is not a polynomial in … with real numeric coefficients.”