Use the Binomial Theorem to Expand the Expression $( 5 a + 4 b ) ^ { 4 }$

question 8

Multiple Choice

Use the Binomial Theorem to expand the expression $( 5 a + 4 b ) ^ { 4 }$ .

• A) \(625 a ^ { 4 } + 256 b ^ { 4 }\)
• B) \(a ^ { 4 } + 4 a ^ { 3 } b + 6 a ^ { 2 } b ^ { 2 } + 4 a b ^ { 3 } + b ^ { 4 }\)
• C) \(625 a ^ { 4 } + 500 a ^ { 3 } b + 400 a ^ { 2 } b ^ { 2 } + 320 a b ^ { 3 } + 256 b ^ { 4 }\)
• D) \(a ^ { 4 } + 16 a ^ { 3 } b + 96 a ^ { 2 } b ^ { 2 } + 256 a b ^ { 3 } + 256 b ^ { 4 }\)
• E) \(625 a ^ { 4 } + 2000 a ^ { 3 } b + 2400 a ^ { 2 } b ^ { 2 } + 1280 a b ^ { 3 } + 256 b ^ { 4 }\)

Calculate and understand the significance of the contribution margin and contribution margin ratio.

Understand the effect of changes in sales volume on costs and profitability.

Determine the operating income under different sales and cost scenarios.

Analyze the impact of changes in fixed and variable costs on the break-even point.

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Definitions:

Production

The process of creating goods or services by combining labor, machinery, and materials resources.

Returns to Scale

The rate at which output increases as inputs are increased proportionally.

Long-Run Average Total Cost

The average cost per unit of output when all input factors are variable, and economies of scale are fully exploited.

Production

The process of creating goods and services from various inputs like labor, knowledge, and raw materials.