Use the Binomial Theorem to Expand and Simplify the Expression $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

question 24

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression.​ $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$ ​

• A) \(2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375\)
• B) \(2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375\)
• C) \(2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375\)
• D) \(2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375\)
• E) \(2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375\)

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Definitions:

Fixed Cost

Costs that do not change with the volume of production, such as rent, salaries, and equipment leases.

Total Cost

The complete cost of production that includes both fixed and variable costs incurred in making a product or providing a service.

Average Variable Cost

The sum of costs that vary with the level of production, distributed over the total number of units produced.

Variable Cost

Expenses in a business that change in proportion with the volume of production or sales, such as materials and labor costs.