What is the meaning of "Subhan Allah wa bihamdihi" and "Bismillah"?

"Subhan Allah" means to declare Allah free from every flaw, deficiency, and evil, and it encompasses a great principle of Tawhid (monotheism). It is derived from as-sabh, meaning distance, i.e., to distance thoughts from attributing any deficiency to Allah. As for "wa bihamdihi" (and with His praise) in "Subhan Allah wa bihamdihi," it means glorification and praise together, i.e., I glorify Allah and I praise Him, or I glorify Him while being in a state of praising Him.