How did the crusades affect the expansion of the Holy Roman Empire?
If you are talking about the Crusades in the Holy Land, then there was no impact on the expansion of the Holy Roman Empire. However, if you are talking about crusades in a broader sense, the Holy Roman Empire did expand via crusades in the 1100s and 1200s. These crusades were carried out not against Muslims in the Holy Land, but against pagans in Eastern Europe.
In these crusades, princes from the German parts of the Holy Roman Empire went out into Eastern Europe and forced the people there to become Christian. This occurred in places that are now parts of Germany, Poland and Finland. Once these places were converted to Christianity, they became part of the Holy Roman Empire.
So if you expand the definition of crusade to include any war fought to spread Christianity, the Holy Roman Empire expanded its territory through crusades in Eastern Europe.