Translation:My two older brothers are both senators.
"både" (meaning both) is part of the fixed expression "både X og Y"
"begge" means both like in this example
Jeg er både studerende og ingeniør (I am both a student and an engineer)
Vi elsker begge at spiser kartofler (We both love to eat potatoes)
Thanks! I noticed that "både" can be used for more than two objects, like "både min mor, min far og min søster" (or something like that). Do you know if this is correct? In English you would use "both" only for exactly two objects ("both my brother and my sister", but not "both my sister, my aunt, my uncle and my friends"), right?