Why did the US try to contain Communism around the world rather than just forcing the Soviets to leave these countries?

The United States committed itself to containing communism immediately after WWI because it appeared as though communism was spreading rapidly. The Soviet Union showed no signs of leaving Eastern Europe. There were reports of oppression against religious groups and nationalists in Eastern Europe. The United States regarded the Soviet regime as being undemocratic and the polar opposite of the American way of life—it was important to ensure that the Soviet Union did not spread further into Europe and leave the United States to one day fight the regime on its own. The United States indirectly opposed Soviet influence by siding with rightist candidates in postwar elections in Italy and France. The United States also funneled money to anticommunists in Greece.

The United States also was fearful of Soviet nuclear capabilities. Stalin did not trust the United States after the US ended the war with Japan with the aid of two atomic weapons. US military planners thought that the Soviet Union was too backward to develop a bomb before 1970; when US spy planes found radioactive isotopes over Soviet airspace, it touched off a search for communist spies inside of American political and military institutions. In order to appear strong against communists, American politicians put more emphasis on defense spending and containment as well as oppressing communist sympathizers at home.

The United States also had additional worries about the spread of communism after Mao's takeover of China. Even though the regime of Chiang Kai-shek was ineffective and corrupt, people were shocked when Mao's revolution took hold in China. There was additional shock when communists in North Korea invaded South Korea. Harry Truman was accused of being soft on communism as the press, led by Time's Henry Luce, stated that the United States "lost China." In order to ensure no further losses, presidents Eisenhower and Kennedy toughened their stance against anything that looked like communist aggression. It was believed that all communists were being directed by the Kremlin, when in reality, many of these communist takeovers were really anti-imperialist movements that used funding from China and the Soviet Union.

answer

explanation

the given equation is

we can rewrite this as:

let

then the equation becomes:

the factors of 8 that sum up to -9 are {-1,-8}

we split the middle term with these factors to obtain,

we factor by grouping to obtain:

apply the zero product property to get:

but