A multivariate polynomial (i.e., a polynomial in more than one variable) with all terms having the same degree. For example, 
is a homogeneous polynomial of degree three.
See also
Polynomial, Polynomial Form, Symmetric Polynomial
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Cite this as:
Weisstein, Eric W. "Homogeneous Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HomogeneousPolynomial.html