can someone explain to me how ending a life is more expensive than keeping them alive?
It takes a lot of lawyers and experts called in to prove without a shadow of a doubt that someone is guilty of something like premeditated murder in the first degree. Copied directly from the Florida Supreme Court definition of First Degree Premeditated Murder:
To prove the crime of First Degree Premeditated Murder, the State must prove the following three elements beyond a reasonable doubt:
1. (Victim) is dead.
2. The death was caused by the criminal act of (defendant).
3. There was a premeditated killing of (victim).
The two penalties for this crime are death and life sentence without the possibility of parole. Once you get to the, "beyond a reasonable doubt" part is where it gets expensive. The lawyers and experts needed to prove this are incredibly expensive for the prosecution. So much so that depending on the state it usually costs more to execute someone than to imprison them for life. It's also worth considering that the unspecific nature of the third element probably is hell on the prosecution when trying to prove it beyond a reasonable doubt.