Completely Factor the Expression $$3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$$

question 5

Multiple Choice

Completely factor the expression. $$3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$$

• A) \(3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)\)
• B) \(3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)\)
• C) \(3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)\)
• D) \(3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)\)
• E)prime

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Definitions:

Social Behavior

Actions among individuals within the same species that are directed towards or influenced by other members of the same species, including cooperation, competition, and communication.

Inclusive Fitness Theory

A concept in evolutionary biology proposing that an organism's genetic success is derived not only from personal reproduction but also from supporting the reproduction of relatives.

Eusociality

A high level of organization in social animals characterized by cooperative brood care, division of labor, and overlapping generations within a colony.

Social Behavior

Interactions among individuals of the same species that influence the behavior of one another, often vital for survival and reproduction.