I stumbled across this problem and I realize that it's propably easy but somehow I can't imagine the problem properly.
Prove that the maximal number of monomials (that are not similar) of polynomial $n$ variables of a degree $d$ is equal to $\binom{n+d}{n}$
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user378298
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I don't understand this line: Let $x1,…,xn$ be the$ n$ variables. The typical term of the polynomial has the form $Cx_1^{k_1}x_2^{k_2}\cdots x_n^{k_n}$ but the monomial of a polynomial has this form: $a_{n}x^n$. Ok I understand, I looked up multivariate polynomial on wolfram – user378298 Aug 15 '18 at 11:27
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1Right. So a multivariate polynomial has as its monomials, terms of the given form. Also, the degree of a monomial is the sum of the degrees of the terms, in this case $k_1 + ... + k_n$. – Sarvesh Ravichandran Iyer Aug 15 '18 at 12:04