Use the Binomial Theorem to Expand and Simplify the Expression $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

question 24

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression.​ $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$ ​

• A) \(2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375\)
• B) \(2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375\)
• C) \(2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375\)
• D) \(2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375\)
• E) \(2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375\)

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Definitions:

Critical Value

A threshold in hypothesis testing that defines the boundary beyond which an observed test statistic is considered statistically significant.

Level of Significance

A threshold used in hypothesis testing that determines the probability of wrongly rejecting a true null hypothesis.

T-test

A statistical method employed to ascertain whether there's a notable difference in the average values of two distinct groups.

Null Hypothesis

A statement positing that there is no significant difference or relationship between specified populations, any observed difference being due to sampling or experimental error.