Use the Binomial Theorem to Expand and Simplify the Expression $( r + 5 s ) ^ { 6 }$

question 405

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression. $( r + 5 s ) ^ { 6 }$

• A) \(r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r - 15625 s ^ { 6 }\)
• B) \(r ^ { 6 } - 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }\)
• C) \(r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }\)
• D) \(r ^ { 6 } - 30 s r ^ { 5 } - 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } - 9375 s ^ { 4 } r ^ { 2 } - 18750 s ^ { 5 } r - 15625 s ^ { 6 }\)
• E) \(r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }\)

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Definitions:

Fannie Mae

A government-sponsored enterprise (GSE) in the United States aimed at expanding the secondary mortgage market by securitizing mortgages into mortgage-backed securities.

Capital Stock

The total amount of physical goods a company owns for the purpose of production, including buildings, machinery, and equipment.

Productivity

The measure of the efficiency of production, often quantified as the ratio of output to input in the production process.

Investment

The purchase or construction of any new plant, equipment, or residential housing, or the accumulation of inventory; represented by I.