The problem involves finding the area of a rectangle with dimensions given as expressions in terms of $x$. Let’s solve this step by step:

Dimensions:

• Length = $5x + 4$
• Width = $4x - 4$

Area of a rectangle formula:

$\text{Area} = \text{Length} \times \text{Width}$

Substitute the given dimensions: $\text{Area} = (5x + 4)(4x - 4)$

Expand the expression:

Use the distributive property: $\text{Area} = 5x(4x) + 5x(-4) + 4(4x) + 4(-4)$

$\text{Area} = 20x^2 - 20x + 16x - 16$

Simplify the terms: $\text{Area} = 20x^2 - 4x - 16$

Final Expression:

The expression that represents the area is: $20x^2 - 4x - 16$

Correct Answer:

The correct choice is B: $20x^2 - 4x - 16$.

Would you like further clarification on the steps or assistance with a related concept? Here are five related questions:

1. How can the distributive property be applied to other geometric shapes?
2. What happens to the area if the dimensions are doubled?
3. How can the quadratic expression $20x^2 - 4x - 16$ be factored?
4. How does this expression change if one dimension is reduced by a constant value?
5. What are the practical applications of expressing areas algebraically?

Tip: Always double-check your expanded terms to ensure accurate simplification.