Write the Binomial Expansion of the Expression $$\left( \frac { 1 } { 3 } x + 5 \right) ^ { 3 }$$

question 425

Multiple Choice

Write the binomial expansion of the expression.
- $$\left( \frac { 1 } { 3 } x + 5 \right) ^ { 3 }$$

• A) \(\frac { 1 } { 9 } x ^ { 3 } + \frac { 5 } { 3 } x ^ { 2 } + 125\)
• B) \(\frac { 1 } { 27 } x ^ { 3 } + \frac { 5 } { 3 } x ^ { 2 } + 25 x + 125\)
• C) \(\frac { 1 } { 9 } x ^ { 3 } + \frac { 5 } { 3 } x ^ { 2 } + 25 x + 125\)
• D) \(\frac { 1 } { 27 } x ^ { 6 } + \frac { 10 } { 9 } x ^ { 3 } + 125\)

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Definitions:

Long-run Equilibrium

A state in which all factors of production and outputs are variable, allowing for the adjustment of all inputs, leading to a balanced economic condition over time.

Zero Economic Profits

Occurs when a firm earns just enough revenue to cover its total costs, including opportunity costs, but no more.

Efficiently

Performing or functioning in the best possible manner with the least waste of time and effort.

Economies of Scale

The cost advantage achieved by businesses when production becomes efficient, as the scale of operation increases leading to a reduction in average costs.