Find the Following Product and Express Your Answer in Simplest $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

question 6

Multiple Choice

Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

• A) \(- 112 \sqrt { 77 } - 44 \sqrt { 7 } + 980 \sqrt { 11 } + 385\)
• B) \(112 \sqrt { 77 } - 44 \sqrt { 11 } - 980 \sqrt { 7 } + 385\)
• C) \(16 \sqrt { 7 } + 4 \sqrt { 11 } - 385\)
• D) \(112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385 \sqrt { 343 }\)
• E) \(112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385\)

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Definitions:

Validation Impulse

The psychological drive to seek recognition, approval, or confirmation from others, often through digital interactions or social media.

Affinity Impulse

The spontaneous preference or attraction toward a person, object, or activity due to perceived similarities or emotional connections.

Motivated

Having a strong desire or willingness to do something, often driven by internal or external factors.

Personal Utility

The subjective value or satisfaction a person derives from using a product or service, based on personal preferences and needs.