Final answer:
The Soviet Union extended their power over Eastern European states by backing the establishment of pro-Soviet communist governments. Yugoslavia, having liberated itself and not being occupied by the Soviet army, maintained its independence from the Soviet bloc under leader Josip Tito.
Step-by-step explanation:
The Soviet Union extended their power over other Eastern European states following World War II primarily through the establishment of communist governments backed by the military and political influence of the USSR.
Stalin ordered the backing of communist parties in countries such as Poland, Czechoslovakia, Hungary, and Romania, leading to the formation of communist governments in these nations. The Soviet Union, although economically strained post-war, used military coercion and political pressure to secure control over these states.
Yugoslavia was different because it liberated itself from Nazi rule and thus was never occupied by the Soviet Army. Consequently, Yugoslavian leader Josip Tito maintained independence from the Soviet bloc, offering a different leftist model from that of Stalin's Soviet Union.
Tito's regime, while still authoritarian and jailing dissenters, resisted being drawn into the Soviet sphere of influence and therefore was never under Soviet control, defying Stalin's attempts to dictate its policies.