Homogeneous Cyclotomic Polynomial is Symmetric

Theorem
Let $n>1$ be a natural number.

Let $\Phi_n(x,y)$ be the $n$th homogeneous cyclotomic polynomial.

Then $\Phi_n(x,y) = \Phi_n(y,x)$, that is, $\Phi_n(x,y)$ is symmetric.