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Use One of the Appropriate Patterns (a+b)2=a2+2ab+b2( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }

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Use one of the appropriate patterns (a+b)2=a2+2ab+b2( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 } ; (ab)2=a22ab+b2( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 } ; (a+b)(ab)=a2b2( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 } to find the following product. (3+9n)(39n)( 3 + 9 n ) ( 3 - 9 n )


Definitions:

Profit-Maximizing Output

The level of production at which a firm achieves the highest possible profit.

Marginal Cost

The cost of producing one additional unit of a product or service.

Average Variable Cost

Average Variable Cost is the variable cost per unit of output, calculated by dividing total variable costs by total output, illustrating how variable costs change with output levels.

Output

The total amount of goods or services produced by a person, machine, factory, country, etc., within a particular time period.

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