Use the Binomial Theorem to Expand the Expression $\left( x ^ { 3 } + 2 y \right) ^ { 4 }$

question 170

Multiple Choice

Use the binomial theorem to expand the expression.
- $\left( x ^ { 3 } + 2 y \right) ^ { 4 }$

• A) \(x ^ { 7 } + 6 x ^ { 6 } y + 24 x ^ { 5 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)
• B) \(x ^ { 12 } + 8 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 32 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)
• C) \(x ^ { 7 } + 8 x ^ { 6 } y + 12 x ^ { 5 } y ^ { 2 } + 8 x ^ { 3 } y ^ { 3 } + 2 y ^ { 4 }\)
• D) \(x ^ { 12 } + 6 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }\)

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Definitions:

Locational Transition Fit

A type of fit defined by tolerances that allows for a limited amount of either interference or clearance between assembled parts.

Clearance

The intentional space or gap between two mating parts to ensure there is no unwanted friction or binding during operation.

Interference Fit

A method of fitting two parts together using a dimension in which the size of the hole is smaller than the size of the shaft to be inserted, creating a high-pressure seal.

Locational Fits

Types of fits defined by standard tolerances that determine how tightly or loosely two parts will connect, particularly regarding their location accuracy.