Look at the image, that should answer your question. Good luck!
Answer:
Colonies wanted to establish their presence in the New World, Colonies would keep other European countries from trying to claim land and Colonies would keep problems with American Indians in the area to a minimum.
Chapultepec, Battle of, and Capture of Mexico City (1847<span>).By </span>12 September 1847<span>, the Mexican War was almost over; the Americans had been victorious in every major engagement, New Mexico had surrendered, U.S. forces had subdued Upper California, and Maj. Gen. Winfield Scott and 7,000 U.S. troops were camped outside </span>