Factor Completely $$27 x ^ { 12 } + 64 y ^ { 12 }$$

question 93

Multiple Choice

Factor completely. $$27 x ^ { 12 } + 64 y ^ { 12 }$$

• A) \(\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)\)
• B) \(\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)\)
• C) \(\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)\)
• D) \(\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 24 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)\)

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Definitions:

Representativeness Heuristic

Representativeness Heuristic is a cognitive shortcut that involves judging the probability of an event by its similarity to a prototype.

Recognition-Primed Decision Making

A model that describes how people make quick, effective decisions by recognizing patterns and similarities with past experiences.

Mental Simulations

The cognitive process of imagining or visualizing a scenario in one's mind to predict outcomes, plan actions, or solve problems.

Deductive Validity

A characteristic of a deductive argument where if the premises are true, the conclusion must also be true, ensuring the argument's logical soundness.