Use the Binomial Theorem to Expand and Simplify the Expression $( x + 5 ) ^ { 6 }$

question 9

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression.​ $( x + 5 ) ^ { 6 }$ ​

• A) \(x ^ { 6 } + 30 x ^ { 5 } + 500 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 15625 x + 625\)
• B) \(x ^ { 6 } + 500 x ^ { 5 } + 375 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625\)
• C) \(x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625\)
• D) \(x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } - 18750 x + 625\)
• E) \(x ^ { 6 } + 30 x ^ { 5 } + 25 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625\)

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Definitions:

GDP PPP

Gross Domestic Product (GDP) measured in terms of the Purchasing Power Parity (PPP), which adjusts for price level differences across countries, providing a more accurate comparison of economic productivity and standards of living.

Infant Mortality

The rate at which babies under one year of age die, considered as an indicator of the health conditions of a population.

Demographic Data

Information related to the characteristics of populations, such as age, race, sex, income level, and employment, widely used in research and policy making.

Total Fertility Rate

The average number of children a woman is expected to have over her lifetime, a key demographic indicator of population growth.