As european settlement began moving farther west and claiming more land. what happened to relations between colonists and american indians?

The colonists and American Indians rarely cooperated. They had many battles, most of which were started by American Indians. They had good reason to, too. When colonists decided to take more land from the west, they also decided to take over American Indian territory. It would be the same as you happily living in a mansion and then all of a sudden some weird dude comes flying and barges into your house, claiming it as their own. You wouldn't like that, would you? So, the battles weren't the American Indians' fault-it was the colonists.
Hope this helps and have a great day!  XD