Use the Binomial Theorem to Expand and Simplify the Expression $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

question 401

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

• A) \(x ^ { 3 } + 1\)
• B) \(x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1\)
• C) \(x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1\)
• D) \(- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1\)
• E) \(x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1\)

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Definitions:

Variable-ratio

A schedule of reinforcement where a response is reinforced after an unpredictable number of responses, making it highly effective for maintaining behaviors.

Fixed Interval

Fixed Interval refers to a schedule of reinforcement where the first response is rewarded only after a specified amount of time has elapsed.

Continuous Reinforcement

A learning process in which a behavior is reinforced every time it occurs, leading to rapid learning.

Variable Ratio

A schedule of reinforcement wherein a response is rewarded after an unpredictable number of responses, used in behavior modification and learning processes.