Use the Binomial Theorem to Expand and Simplify the Expression $( 4 x + 3 y ) ^ { 4 }$

question 46

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 3 y ) ^ { 4 }$

• A) \(256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }\)
• B) \(256 x ^ { 4 } + 4 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + y ^ { 4 }\)
• C) \(256 x ^ { 4 } + 108 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }\)
• D) \(x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }\)
• E) \(256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + 81 y ^ { 4 }\)

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Definitions:

Closed-Loop

Closed-Loop refers to a system or process that uses feedback to control states or outputs, aiming for stable operation and error correction.

Open-Loop System

A control mechanism that operates without using feedback to adjust its input based on the outputs.

More Complex

Referring to a system or process that has a greater level of intricacy or difficulty.

Servo Drive

A special electronic amplifier used to power and control servomechanisms, providing precise control of angular or linear position, velocity, and acceleration.