Factor Using the Ac-Method $$84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$$

question 12

Multiple Choice

Factor using the ac-method.
- $$84 x ^ { 2 } + 49 x y + 7 y ^ { 2 }$$

• A) prime
• B) \(( 21 x + 7 y ) ( 4 x + y )\)
• C) \(7 ( 3 x - y ) ( 4 x - y )\)
• D) \(7 ( 3 x + y ) ( 4 x + y )\)

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Definitions:

Staggered Conformation

An arrangement of atoms in a molecule where groups attached to adjacent carbons are as far apart as possible, minimizing steric strain.

Ethane

A simple alkane with the chemical formula C2H6, consisting of two carbon atoms single-bonded together, surrounded by hydrogen atoms.

Butane Conformers

Different spatial arrangements of atoms in butane that result from rotation around single bonds, affecting the molecule's energy.

Energy Minima

Points in a potential energy surface that represent stable states of a system, where any small displacement of particles leads to an increase in potential energy.