Use the Binomial Theorem to Expand and Simplify the Expression $( 2 x + y ) ^ { 3 }$

question 56

Multiple Choice

Use the Binomial Theorem to expand and simplify the expression.​ $( 2 x + y ) ^ { 3 }$ ​

• A) \(8 x ^ { 3 } - 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }\)
• B) \(8 x ^ { 3 } + 12 x ^ { 2 } y - 6 x y ^ { 2 } + y ^ { 3 }\)
• C) \(x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }\)
• D) \(8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }\)
• E) \(8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } - y ^ { 3 }\)

---

Definitions:

Polymer

Large molecules composed of repeating structural units (monomers) bonded together, exhibiting a broad range of chemical and physical properties.

Neoprene

A synthetic rubber produced by the polymerization of chloroprene, noted for its chemical stability and used in various products such as wetsuits and hoses.

Addition Polymer

A type of polymer formed by the sequential addition of monomer units with unsaturated bonds, such as olefins, to form long chains without the loss of any small molecules.

Condensation Polymer

A type of polymer formed by the condensation reaction where two molecules combine with the elimination of a small molecule, often water, between them.