Expand the Expression Using the Binomial Theorem $$( 2 x + 1 ) ^ { 5 }$$

question 184

Multiple Choice

Expand the expression using the Binomial Theorem.
- $$( 2 x + 1 ) ^ { 5 }$$

• A) \(\left( 4 x ^ { 2 } + 4 x + 1 \right) ^ { 5 }\)
• B) \(32 x ^ { 5 } + 80 x ^ { 4 } + 80 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1\)
• C) \(32 x ^ { 5 } + 10 x ^ { 4 } + 40 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1\)
• D) \(32 x ^ { 5 } + 16 x ^ { 4 } + 8 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 1\)

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Definitions:

2,2,4-Trimethyl-3-pentanone

A chemical compound with the molecular formula C8H16O, serving as a ketone with its carbonyl group located on the third carbon atom.

Enolizable Ketone

A ketone capable of tautomerizing to an enol, which is a compound with a double bond and an alcohol group.

Enolate Salt

A negatively charged ion formed by the deprotonation of an alpha-carbon of a carbonyl compound, involved in various organic synthesis reactions.

Lithium Diisopropylamide

A strong non-nucleophilic base, represented as LDA, used in organic synthesis for deprotonation reactions.