I got stuck on a polynomial problem, and decided to search up the solution. I found someone else here who asked it a while ago, but I can't understand their answer.(link: Find all integers $a,b,c,d$ such that $a+b+c+d=0$ and $a^3 + b^3 + c^3 + d^3 =24$.)
This part specifically:
In my attempt, I managed to arrive at the same conclusion that $ab(a+b)+cd(c+d)=-8$, but was not able to continue further. This factorization doesn't even seem to make sense. Can anyone help me understand?