Answer:
Lay claims to land acquisition.
Lay claim to attain more wealth.
Lay claim to colonize more lands to expand empire
Explanation:
The main three goals that the Spanish has in the Expedition to the North side of Americans were that:
The Spanish were so desired to attain certain level of massive riches in wealth
To lay claims to lands as much as they can lay claimed to.
The Spanish were determined to colonize lands as much as their power can get as as to expand her empire.