Use the Binomial Theorem to Expand the Expression $\left( x ^ { 3 } + 2 y \right) ^ { 4 }$

question 170

Multiple Choice

Use the binomial theorem to expand the expression.
- $\left( x ^ { 3 } + 2 y \right) ^ { 4 }$

• A) \(x ^ { 7 } + 6 x ^ { 6 } y + 24 x ^ { 5 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)
• B) \(x ^ { 12 } + 8 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 32 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)
• C) \(x ^ { 7 } + 8 x ^ { 6 } y + 12 x ^ { 5 } y ^ { 2 } + 8 x ^ { 3 } y ^ { 3 } + 2 y ^ { 4 }\)
• D) \(x ^ { 12 } + 6 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)

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Definitions:

Dendrite

Dendrites are branched extensions of a neuron that receive signals from other neurons and transmit them towards the cell body.

Node of Ranvier

Gaps in the myelin sheath along the axon of neurons where action potentials are generated.

Neurotransmitters

Chemical substances that transmit signals across a synapse from one neuron to another neuron or cell in the body.

Synaptic Vesicle

A small, spherical structure found within nerve cell endings, responsible for storing neurotransmitters that are released during synaptic transmission.