Use the Binomial Theorem to Expand the Expression $\left( \frac { 2 } { x } + 2 y \right) ^ { 5 }$

question 75

Multiple Choice

Use the Binomial Theorem to expand the expression. Simplify your answer. $\left( \frac { 2 } { x } + 2 y \right) ^ { 5 }$

• A) \(\frac { 32 } { x ^ { 5 } } - \frac { 240 y } { x ^ { 4 } } + \frac { 720 y ^ { 2 } } { x ^ { 3 } } - \frac { 1080 y ^ { 3 } } { x ^ { 2 } } + \frac { 810 y ^ { 4 } } { x } - 243 y ^ { 5 }\)
• B) \(\frac { 32 } { x ^ { 5 } } - \frac { 160 y } { x ^ { 4 } } + \frac { 320 y ^ { 2 } } { x ^ { 3 } } - \frac { 320 y ^ { 3 } } { x ^ { 2 } } + \frac { 160 y ^ { 4 } } { x } - 32 y ^ { 5 }\)
• C) \(\frac { 1024 } { x ^ { 5 } } + \frac { 3840 y } { x ^ { 4 } } + \frac { 5760 y ^ { 2 } } { x ^ { 3 } } + \frac { 4320 y ^ { 3 } } { x ^ { 2 } } + \frac { 1620 y ^ { 4 } } { x } + 243 y ^ { 5 }\)
• D) \(\frac { 243 } { x ^ { 5 } } - \frac { 810 y } { x ^ { 4 } } + \frac { 1080 y ^ { 2 } } { x ^ { 3 } } - \frac { 720 y ^ { 3 } } { x ^ { 2 } } + \frac { 240 y ^ { 4 } } { x } - 32 y ^ { 5 }\)
• E) \(\frac { 32 } { x ^ { 5 } } + \frac { 160 y } { x ^ { 4 } } + \frac { 320 y ^ { 2 } } { x ^ { 3 } } + \frac { 320 y ^ { 3 } } { x ^ { 2 } } + \frac { 160 y ^ { 4 } } { x } + 32 y ^ { 5 }\)

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Definitions:

White Rami Communicantes

Nerve fibers connecting the spinal nerves to the sympathetic chain, important for the sympathetic nervous system's responses.

Preganglionic Axons

Axons of nerve cells that originate in the central nervous system and extend to a ganglion, transmitting nerve impulses.

Sympathetic Chain

A part of the sympathetic nervous system consisting of a series of interconnected ganglia located along the vertebral column.

ANS

Autonomic Nervous System; a control system that acts largely unconsciously and regulates bodily functions such as the heart rate, digestion, respiratory rate, pupillary response, urination, and sexual arousal.