The problem is

Sorry I'm new. That's the best I could write the problem. It's easy to find the determinant with expansion by minors but to get the simplified solution involves some sort of clever trick that I don't know of. Here's what I can get to.

There are many ways to factor out terms from this.

There are even more ways of course. None of these ways lead me to the simple solution:

Can someone explain how to factor this? Thanks.