Which of the following expressions are polynomials in one variable and which are not? State reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{2}+2xy+y^{2}$

(D) The given expression is $x^{2}+2xy+y^{2}$.
$1$. $A$ polynomial is an algebraic expression in which the exponents of the variables are non-negative integers (whole numbers).
$2$. In the given expression,the exponents of $x$ and $y$ are $2, 1,$ and $0$,which are all whole numbers. Therefore,it is a polynomial.
$3$. However,the expression contains two distinct variables,$x$ and $y$.
$4$. Since it contains more than one variable,it is not a polynomial in one variable.