Use the Binomial Theorem to Expand the Expression $( 4 x + 1 ) ^ { 5 }$

question 5

Multiple Choice

Use the binomial theorem to expand the expression.
- $( 4 x + 1 ) ^ { 5 }$

• A) \(1024 x ^ { 5 } + 1\)
• B) \(1024 x ^ { 5 } + 256 x ^ { 4 } + 64 x ^ { 3 } + 16 x ^ { 2 } + 4 x + 1\)
• C) \(1024 x ^ { 5 } + 20 x ^ { 4 } + 160 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1\)
• D) \(1024 x ^ { 5 } + 1280 x ^ { 4 } + 640 x ^ { 3 } + 160 x ^ { 2 } + 20 x + 1\)

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Definitions:

Resource-Holding Potential

The ability of an organism to defend resources such as food, territory, or mates against competitors, which can affect its reproductive success.

Territorial Disputes

Conflicts between individuals or groups over the possession or control of land or resources.

Payoff Asymmetry Hypothesis

The theory that the differing costs and benefits of a decision or action can influence the behavior of individuals in competitive and cooperative interactions.

Resource-Holding Potential

Resource-holding potential is an individual animal's ability to acquire and defend resources against competitors, often influencing mating success.