How did Alaska and Hawaii in the United States merge into the territory of the United States?

When the United States just left Britain, its territory was limited to 13 States along the Atlantic coast, with an area of only 940,000 square kilometers. 1783 After the War of Independence ended, Britain announced that it would give up other territories east of the Mississippi River and bring them into the territory of the United States, but this was not enough for the development of its capitalism, so the United States quickly embarked on the road of outward expansion and continued to expand westward and southward by taking advantage of the melee of European colonists. They seized the colonies of Spain, France and Britain through threats of war, fraud and preemptive measures, annexed a large number of Mexican land, and expanded westward to the Pacific coast and southward to the Gulf coast. 1867, Alaska and Aleutian Islands were purchased from Russia. 1898, Hawaii was annexed. The territory of the United States is expanding year by year. In less than a century, the territory has expanded by 10 times, reaching an area of more than 9.363 million square kilometers, accounting for about half of the North American continent. It has become the second largest country in the American continent, second only to Canada, and fourth in the world, which is about 40 times that of Britain and slightly smaller than that of Europe. 1783, Britain not only recognized the independence of 13 colony, but also gave a rectangular piece of land to the west of 13 colony and east of Mississippi River to the United States. In the early days of the People's Republic of China, the territory of the United States started from the Atlantic coast in the east, the Mississippi River in the west, the Spanish colony Florida Peninsula in the south and the British colony Canada in the north, covering an area of more than 2.3 million square kilometers, equivalent to 1/4 of the current territory of the United States. 1803, Jefferson, the third president of the United States, bought a large piece of land in Greater Louisiana for150,000 dollars through negotiations under the pressure of the Haitian black independence movement and the European anti-French alliance. In 2009, the United States spent $5 million to buy150,000 from Spain. After the establishment of the Republic of Texas, it proposed to merge with the United States, and became the 28th state of the United States on February 29th 1845 1845. The merger of Texas by the United States angered Mexico, and Mexico immediately severed its relations with the United States. 1846, the us-Mexico war broke out. The progress of the war is extremely unfavorable to Mexico. 1On September 7th, 847, American troops captured Mexico City, the capital of Mexico. At the beginning of 1848, the war ended in Mexico's defeat and the United States and Mexico signed a treaty. According to the treaty, Mexico gave up its claim to Texas 1.0 1.000 square kilometers and ceded 1.37 million square kilometers of land to the United States, including California, Nevada, Utah, Arizona, New Mexico and western Florida. 1853, 1853 On February 30th, the United States bought a strip of land with an area of 77,000 square kilometers from Mexico, which was called gadsden. After the acquisition of gadsden, the United States annexed 2.4 million square kilometers of Mexican land.