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Let $$f(x)=a_0x^n+a_1x^{(n-1)}y+a_2x^{(n-2)}y^2...+a_{(n-1)}xy^{(n-1)}+a_ny^n$$ $$g(x)=b_0x^n+b_1x^{(n-1)}y+b_2x^{(n-2)}y^2...+b_{(n-1)}xy^{(n-1)}+b_ny^n$$ If $$f(x)=g(x)$$ for all x and y. Does $$a_i=b_i$$

And, what if I include terms with power less than n?

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1 Answer 1

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Yes. Set $y=1$, then the problem is reduced to a single variable polynomial. For your second question, you might need to work with a finite set of $y's$ to get the needed result.

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