Europeans sought to spread their religion to indigenous peoples in the Americas through preaching, trade, and taking over indigenous people's lands, is the right answer.
The spread of cultural beliefs from one group to another is most commonly known as the Cultural diffusion, through which people became more reach culturally. Religion was one of the important motives for the age of Exploration. Not only Europeans but also others committed to spreading their religion in the new world. Of course, spreading of the religion was an important cause behind the exploration, but the fact, that some expeditions were the result of religious freedom of the Native Europeans in the New World cannot be denied. The desire to gain money from trade resulted in their first exploration. Europeans wanted to detour Muslim controlled trade routed and to trade directly with the East for their spices and skills or expertise.