Which of the following expressions is a polynomial,and state the reason? If an expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{3}+3 x^{2} y+3 x y^{2}+y^{3}$

(N/A) The expression $x^{3}+3 x^{2} y+3 x y^{2}+y^{3}$ is a polynomial because all the exponents of the variables $x$ and $y$ are non-negative integers. Since it contains two distinct variables,$x$ and $y$,it is a polynomial in two variables,not a polynomial in one variable.