Expand the Binomial by Using the Binomial Theorem $$\left( e ^ { x } - e ^ { - x } \right) ^ { 4 }$$

question 46

Multiple Choice

Expand the binomial by using the binomial theorem.
- $$\left( e ^ { x } - e ^ { - x } \right) ^ { 4 }$$

• A) \(e ^ { 4 x } + 4 e ^ { 3 x } + 6 e ^ { 2 x } + 4 e ^ { x } + 1\)
• B) \(e ^ { 4 x } + 4 e ^ { 2 x } + 6 + \frac { 4 } { e ^ { 2 x } } + \frac { 1 } { e ^ { 4 x } }\)
• C) \(e ^ { 4 x } - 4 e ^ { 3 x } + 6 e ^ { 2 x } - 4 e ^ { x } + 1\)
• D) \(e ^ { 4 x } - 4 e ^ { 2 x } + 6 - \frac { 4 } { e ^ { 2 x } } + \frac { 1 } { e ^ { 4 x } }\)

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Definitions:

Probability

A numerical assessment between 0 and 1 indicating how probable it is for an event to take place.

Expected Value

The weighted average of all possible values of a random variable, with weights being their respective probabilities.

Probability

A measure quantifying the likelihood of a specific event occurring, often expressed as a number between 0 and 1.

Von Neumann-Morgenstern Utility Function

A utility function that assumes individuals can rank their preferences under uncertainty, used in expected utility theory to describe choices.