Factor the Sum or Difference of Two Cubes $54 x ^ { 3 } - 128 x ^ { 6 }$

question 69

Multiple Choice

Factor the sum or difference of two cubes.
- $54 x ^ { 3 } - 128 x ^ { 6 }$

• A) \(2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 12 x + 16 x ^ { 2 } \right)\)
• B) \(2 \left( 3 x + 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } - 12 x ^ { 3 } + 16 x ^ { 4 } \right)\)
• C) \(2 \left( 3 x - 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } + 12 x ^ { 3 } + 16 x ^ { 4 } \right)\)
• D) \(2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 16 x ^ { 2 } \right)\)

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Definitions:

Weber Fraction

A constant proportion in Weber's Law that describes the smallest change in a stimulus that can be detected as a proportional part of the original stimulus.

Psychological Magnitude

The quantifiable aspect of a psychological factor, such as the intensity of a sensation, emotion, or perception.

Standard Stimulus

A stimulus used as a benchmark in experiments to measure how different stimuli can influence behavior or perception compared to this control stimulus.

Constant

A value or quantity that remains unchanged within a given context or under specified conditions.