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The image contains a question about calculating the area of a rectangle with dimensions given in algebraic expressions. Let’s solve it:

The rectangle's dimensions are:
- Length: \( x + 5 \)
- Width: \( 4x - 3 \)

### Step 1: Formula for the area of a rectangle
The area \( A \) of a rectangle is given by:
\[
A = \text{length} \times \text{width}
\]

### Step 2: Substituting the expressions
\[
A = (x + 5)(4x - 3)
\]

### Step 3: Expanding the expression
Using distributive property:
\[
A = x(4x - 3) + 5(4x - 3)
\]
\[
A = 4x^2 - 3x + 20x - 15
\]
\[
A = 4x^2 + 17x - 15
\]

### Final Answer:
The area of the rectangle is:
\[
\boxed{4x^2 + 17x - 15}
\]

Would you like further clarification or a breakdown of the expansion process?

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Here are 5 related questions to deepen your understanding:
1. How do you determine the area of a rectangle with polynomial dimensions?
2. What does the distributive property mean in algebra?
3. Can the expression \( 4x^2 + 17x - 15 \) be factored further?
4. How would the problem change if one dimension were a constant?
5. What is the importance of combining like terms when simplifying?

**Tip:** Always organize polynomial terms in descending order for clarity.

What is the area of the rectangle given its dimensions: length = x + 5 and width = 4x - 3?

Learn how to calculate the area of a rectangle with dimensions expressed as polynomials. This example uses algebraic expansion and the distributive property to determine the result. Suitable for Grades 8-10.

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