Back in my college days I used to start my practice sessions by going over the most difficult parts of the repertoire I was preparing. That usually meant rapid 16th-note passages which involved both hands. I played them VERY SLOWLY so they also served as warm-ups. Many Beethoven Sonatas have such passages and here is a warm up I fashioned for you from an excerpt of the exuberant 1st movement of Op. 2 #3.
It’s always comfortable and freeing to practice similar motions with both hands: a natural balance of the arms and torso muscles is achieved and it’s easier to relax. So here I have both hands playing the right-hand part for measures 1/2 and 5/6, fill in Beethoven’s left-hand part in measures 3/4 and 7/8 with octaves and have both hands playing the left-hand part in measures 9/10. This exercise feels good and will help you with stretches, octaves, 5th finger strength, broken chords and some close-position finger work as well.
Please remember to play slowly, use a rotating motion of the hands and forearms to help your octaves along and, above all, RELAX EVERYTHING ABOVE YOUR WAIST except your fingers. That includes your facial muscles as well – a “Mona Lisa smile” will help. 😀