Expand the Expression Using the Binomial Theorem $$( 2 x + y ) ^ { 6 }$$

question 41

Multiple Choice

Expand the expression using the Binomial Theorem.
- $$( 2 x + y ) ^ { 6 }$$

• A) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }\)
• B) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }\)
• C) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }\)
• D) \(2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }\)

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Definitions:

Probability

A measure of the likelihood of a particular event's occurrence, ranging from 0 (impossible) to 1 (certain).

P < 0.05

Indicates that the probability of the observed data, or more extreme, occurring by chance is less than 5%, commonly used to determine statistical significance in hypothesis testing.

Population Standard Deviation

The square root of the variance in the full population, indicating how much each member of this population deviates from the population mean.

Sample Standard Deviation

A measure of the amount of variation or dispersion of a set of values in a sample from its mean.