They are correct, and they mean the same thing. The part that says "had washed" shows that the washing happened before the eating. The part that says "before" shows that the washing happened before the eating.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Mercyful_fate let's say I'm eating on the plate right now and my mom asked me "did you wash your plate?"It's a current situation, so "had washed" is not appropriate. Say, "I washed the plate before I started to eat from it".