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

question 318

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:

ATC

Average Total Cost, which is calculated by dividing the total cost of production by the quantity of output produced. It includes both fixed and variable costs.

MC

Marginal Cost, which refers to the increase or decrease in the total cost of production when the output is adjusted by one additional unit.

AVC

Average Variable Cost, representing the variable costs (costs that change with production volume) per unit of output in economics.

ATC

Average Total Cost, which is the total cost divided by the quantity produced, encompassing both fixed and variable costs.