Find the Product $x y \left( 5 x + 4 x y - y ^ { 2 } \right) - 4 x y ^ { 2 } ( 4 x - x y + 5 y )$

question 184

Multiple Choice

Find the product. $x y \left( 5 x + 4 x y - y ^ { 2 } \right) - 4 x y ^ { 2 } ( 4 x - x y + 5 y )$

• A) \(5 x ^ { 2 } y - 4 x ^ { 2 } y ^ { 2 } - x ^ { 3 } + 12 x ^ { 2 } y ^ { 3 } - 21 y ^ { 3 }\)
• B) \(5 x ^ { 2 } y - 12 x ^ { 2 } y ^ { 2 } + 4 x ^ { 2 } y ^ { 3 } - 21 x y ^ { 3 }\)
• C) \(5 x ^ { 2 } y - 12 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } - 21 x y ^ { 3 }\)
• D) \(5 x ^ { 2 } y - 21 x ^ { 2 } y ^ { 2 } - x ^ { 3 } + 4 x ^ { 2 } y ^ { 3 } + 12 x y ^ { 3 }\)
• E) \(5 x ^ { 2 } y ^ { 2 } - 12 x ^ { 2 } y ^ { 2 } + x y ^ { 3 } + 4 x ^ { 2 } y ^ { 2 } - 21 x y ^ { 2 }\)

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Definitions:

Tragedy Commons

The Tragedy of the Commons is an economic theory suggesting that individuals acting in their own self-interest can deplete shared resources, leading to negative outcomes for the whole group.

Fish Population

Refers to the number and varieties of fish within a particular body of water or ecosystem.

Garrett Hardin

An ecologist known for his work on environmental issues and for popularizing the concept of the "tragedy of the commons," which describes the problem of individuals overexploiting a shared resource.

Tragedy of the Commons

A situation in which individual users, acting independently according to their own self-interest, deplete or spoil shared resources through their collective action.