66We say that an expression f(x_1,x_2,\ldots, x_n) in n variables is symmetrical w.r.t. these variables, if interchanging any pair of them leave the value of the expression unchanged.
For instance, the expression f(x,y,z)=xy+yz+zx is symmetric w.r.t. x,y,z. You should note that the expression
g(x,y,z)=A(x+y+z)
is the only symmetric function in three variables of degree 1. (Here A is some constant)
Similarly,
g_1(x,y,z)=A(x^2+y^2+z^2) and g_2(x,y,z)=A(xy+yz+zx) are the only symmetrical functions in three variables of degree 2.
As for the examples you gave, probably now you can answer both your queries.
