Are the verbs in the following sentence grammatically correct?I finished my homework before I practiced the piano.

The above correct sentence may also
be rewritten to include the past perfect tense:

"I had
finished my homework before I practiced the piano."

Using
the past perfect tense allows the writer to communicate that an action occurred before
another action that also happened in the past.  The perfect tenses allow events to be
placed in sequential order so that the listener/reader understands the proper sequence
of events.  Leaving the sentence in the simple past makes the sentence more
ambiguous--the listener/reader relies on the word "before" to put the events in
sequential order.  Using the perfect tense allows for more precise meaning if you are
not speaking about the immediate past.

I have attached a
link to an online writing lab that gives further information about the use of the
perfect tenses.