Answer:
B. to avoid a bloody and costly invasion of Japan
C. to send a message of military strength to the Soviet Union
Explanation:
The Allied plan to invade the Japanese home islands was predicted to have caused hundreds of thousands of casualties if it were to have been carried out. The atomic bombing of the cities of Hiroshima and Nagasaki further forced Japan into an unconditional surrender to prevent further casualties on both sides.
Although not its direct or stated intention, some historians say the atomic bombings were a show of force that also served to dissuade Soviet Union influence in East Asia.