Factor the Sum or Difference of Two Cubes $16 \mathrm { k } ^ { 3 } \mathrm {~m} - 54 \mathrm {~m} ^ { 4 }$

question 145

Multiple Choice

Factor the sum or difference of two cubes.
- $16 \mathrm { k } ^ { 3 } \mathrm {~m} - 54 \mathrm {~m} ^ { 4 }$

• A) \(2 m ( 2 k - 3 m ) \left( 4 k ^ { 2 } + 6 k m + 9 m ^ { 2 } \right)\)
• B) \(2 \mathrm {~m} ( 8 \mathrm { k } - 3 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 6 \mathrm {~km} + 9 \mathrm {~m} ^ { 2 } \right)\)
• C) \(\left( 4 k m - 6 m ^ { 2 } \right) \left( 4 k ^ { 2 } + 9 m ^ { 2 } \right)\)
• D) \(2 m \left( 2 k + 3 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 6 k m + 9 k ^ { 2 } \right)\)

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Definitions:

Production Possibilities

The different quantities of goods that an economy can produce using all available resources and technology effectively.

Gain From Trade

The benefits that countries or individuals obtain by engaging in international trade, allowing for the consumption of more goods and services than would be possible without trade.

Opportunity Cost

The loss incurred from ignoring the subsequent best alternative in a decision-making scenario.

Constant Rate

A steady, unchanging rate of change in a mathematical or economic process.