No, this will not happen. In fact, there was a time when Mexico was a dominant power, owning much of the southwestern territories, including land in what later became the states of California, Nevada, New Mexico, and Utah; Mexico also governed Texas, which tried to declare its independence. When Texas was annexed by the United States in 1845, a war between Mexico and the US broke out, but the United States won, and in 1848, Texas officially became part of the USA, as did the other previously mentioned states.
Over the years, the United States and Mexico have had a complicated relationship. After the Mexican-American war, there were still tensions between the two countries, and in the early 1900s, it seemed war might break out again. But the issues that were causing the two countries to be hostile towards each other were ultimately resolved and the US and Mexico finally became allies.
That said, there are a number of problems that still remain -- illegal Immigration from Mexico to the United States, and the flow of illegal drugs across the border are two of the most contentious. But despite such problems, there is no evidence that the United States wants a war with Mexico. Numerous American and Mexican presidents have maintained very friendly diplomatic relationships, and the two countries have worked together on a number of occasions. Therefore, it is not likely that the United States will attack Mexico and try to capture it, nor is there much evidence that Mexico wants to attack the United States.
Nothing: the US took those territories by the means of war.
mexico
Texas & New Mexico.
Texas, New Mexico, and Arizona.
Puerto Rico is not in Mexico. It is a US Territory in the Caribbean where it is a part of the Greater Antilles.
Britain & Mexico
California, Texas and parts of Arizona and New Mexico.
Mexico
Mexico
California and New Mexico.
Oregón and texas
New Mexico was lost by Mexico during the Mexican-American War (1846-1848). Later, some territories on southern New Mexico were sold by Mexico to the US at the Gadsden Purchase (1854).