Find the Indicated Term or Coefficient of the Binomial Expansion $( x + 2 y ) ^ { 12 }$

question 212

Multiple Choice

Find the indicated term or coefficient of the binomial expansion.
-Find the 11th term of the expansion of $( x + 2 y ) ^ { 12 }$ .

• A) \(33,792 x ^ { 2 } y ^ { 11 }\)
• B) \(33,792 \times 10 y ^ { 2 }\)
• C) \(67,584 \mathrm { x } ^ { 10 } \mathrm { y } ^ { 2 }\)
• D) \(67,584 x ^ { 2 } y 10\)

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Definitions:

Average Variable Cost

The total variable cost divided by the quantity of output, reflecting the cost of labor and materials directly involved in production.

U-shaped

A term often describing a graph or relationship where a variable initially decreases, reaches a minimum point, and then increases, resembling the shape of the letter "U."

Total Product Curve

A graphical representation that shows the relationship between the total output produced by a firm and the quantity of a variable input for a given level of fixed input(s).

Average Product

The output produced per unit of a resource employed, calculated by dividing total product by the quantity of the resource used.