how did the united states purchase lands or rights from latin american countries for everyones benefit?

Answer 1

Both the Texas territories and the California lands were attempting to break away from Mexico in the first place. Most of the "Americans" who fought or died in the Mexican-American war were actually Mexican citizens or Tejanos, including Jim Bowie and Sam Houston. California, essentially ignored by the Mexican government, had declared itself an independent republic from Mexico, though Mexico refused to acknowledge it . The treaty to grant the Southwest sovereignty and freedom from Mexico was a benefit of those who lived there and fought for separation from Mexico.

The purchase of the territories by the US offered protection and a legal system of an intact government, territorial independence, and commercial participation that the Mexican government failed to provide. Bear in mind, France, England, and even Russia were still establishing colonies in the "new" world.

Answer 2

it means we have the chance to meet and fall deeply in love.