What is the difference between "Polynomial" and "Multinomial" in two or more variables?
Since, by definition:
An algebraic expression having two or more (unlike) terms is called a Multinomial.
$5x^2 - 2x$ is a multinomial having $2$ terms,
$5x^3- 2xy + 7y^2$ is a multinomial having $3$ terms,
$7xy - 9yz + 6zx - 7$ is a multinomial having $4$ terms.
Polynomials in two or more variables:
An algebraic expression in two or more variables is called a Polynomial if the Power of every variable in each term is a whole number.
Some books say "Multinomial" is one of the types of "Polynomial", and the other discuss it in particular.
Is the function $f$ cross "Polynomial" or "Multinomial"? Why?
$$f(x, y)=x y + y^2 + 2 x y^2 + y^3 - 3 x y^3 + x y^4,$$