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

question 367

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:

Symmetry-Allowed

In quantum chemistry, a process or transition is symmetry-allowed if it does not violate symmetry rules governing molecular transformations.

Reaction Outcome

The final products, yields, and implications of a chemical reaction based on the reactants and conditions employed.

Major Organic Product

The primary substance produced with the highest yield in a reaction involving organic compounds.

Organic Reaction

A chemical reaction involving organic compounds, leading to the transformation or creation of new organic molecules.