Use the Binomial Theorem to Expand and Simplify the Expression $( 4 x + 5 y ) ^ { 4 }$

question 29

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

• A) \(256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }\)
• B) \(256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }\)
• C) \(256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }\)
• D) \(256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }\)
• E) \(x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }\)

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Definitions:

Amino Acid

Organic compounds that combine to form proteins, serving as the building blocks of life.

Ammonia

A colorless gas with a characteristic pungent smell, used in many industrial and cleaning products, which is toxic in high concentrations.

Urea

Urea is a nitrogenous compound produced in the liver as a waste product of protein metabolism and excreted in urine.

Beta Oxidation

A metabolic process in which fatty acid molecules are broken down in the mitochondria to generate acetyl-CoA, which enters the citric acid cycle to produce energy.