Find the 3rd Term in the Binomial Expansion $$\left( x + \frac { y } { 2 } \right) ^ { 8 }$$

question 7

Multiple Choice

Find the 3rd term in the binomial expansion. $$\left( x + \frac { y } { 2 } \right) ^ { 8 }$$

• A) \(\quad 28 x ^ { 6 } y ^ { 2 }\)
• B) \(\quad 4 x ^ { 6 } y ^ { 2 }\)
• C) \(\quad x ^ { 6 } y ^ { 2 }\)
• D) \(7 x ^ { 6 } y ^ { 2 }\)
• E) \(\quad 7 x ^ { 2 } y ^ { 6 }\)

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Definitions:

Rational Choices

Decision-making based on logical evaluation of outcomes and choosing the option that maximizes benefit or utility.

Inefficient Outcomes

Situations in which resources are not allocated optimally, leading to lost potential welfare or value.

First-Mover Advantage

The competitive advantage gained by the first significant company to move into a new market.

Sequential-Move Game

A strategic game where players make their decisions one after another, with later players having knowledge of previous actions.