Find the Indicated Term or Coefficient of the Binomial Expansion $( x - 2 ) ^ { 13 }$

question 217

Multiple Choice

Find the indicated term or coefficient of the binomial expansion.
-Find the 8 th term of the expansion of $( x - 2 ) ^ { 13 }$ .

• A) \(109,824 x ^ { 6 }\)
• B) \(109,824 x ^ { 7 }\)
• C) \(- 219,648 x ^ { 7 }\)
• D) \(- 219,648 x ^ { 6 }\)

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Definitions:

Missouri Compromise

Deal proposed by Kentucky senator Henry Clay in 1820 to resolve the slave/free imbalance in Congress that would result from Missouri’s admission as a slave state; Maine’s admission as a free state offset Missouri, and slavery was prohibited in the remainder of the Louisiana Territory north of the southern border of Missouri.

Railway System

A network of tracks on which trains run, serving as a critical infrastructure for the transport of passengers and goods over land, significantly contributing to economic development and urbanization.

American Economy

The economic system of the United States, characterized by a mixed economy that includes private freedom combined with centralized economic planning and government regulation.

Urbanization

The process by which towns and cities are formed and become larger as more people begin living and working in central areas, leading to various social, economic, and environmental changes.