Let $d$ be a natural number greater than or equal to $3$. I have the following polynomial $$ F(x_1, ..., x_3) = x_1^d + x_2^d - x_3^d - ( x_1 +x_2 - x_3 )^d. $$ I am trying to figure out if this polynomial is irreducible over $\overline{\mathbb{Q}}$ or not? (Here $\overline{\mathbb{Q}}$ is the algebraic closure of $\mathbb{Q}$)
I would greatly appreciate some assistance! Thank you very much!
PS This is obtained by intersecting $x_1^d + x_2^d - x_3^d - x_4^d = 0$ and $x_1 + x_2 -x_3 - x_4 = 0$.