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I have tried to start with a polynomial with $2$ variables and with degree $2$; it was simple.

But with degree $n$ is much harder. I would like to know the general form not only with $2$ variables but with $m$ variables.

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1 Answer

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Hint: $$\sum_{i_1+i_2+i_3+…i_m\le n}a_{i_1i_2i_3…i_m}x_1^{i_1}x_2^{i_2}…x_m^{i_m}$$ as ${i_k} $ varies through non-negative integers...

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