Irreducibility of $x^{3}-3(p+q)x^{2}+3(p^{2}+q^{2})x-(p^{3}+q^{3})$ for positive integers $p$ and $q$.

Question

Let $p$ and $q$ be positive integers. How can I show that the polynomial $x^{3}-3(p+q)x^{2}+3(p^{2}+q^{2})x-(p^{3}+q^{3})$ is irreducible over the integers?

Answer 1

Hint:

The equation is

$$(x-p)^3+(x-q)^3=x^3.$$