`r gt s`
`{:("Quantity A","Quantity B"),((r+s)(r-s),(s+r)(s-r)):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to compare the two quantities given the condition \( r > s \).

### Step-by-Step Solution:

1. **Understand the Quantities**:
- Quantity A: \( (r + s)(r - s) \)
- Quantity B: \( (s + r)(s - r) \)

Since \( s + r = r + s \), we can rewrite Quantity B as:
- Quantity B: \( (r + s)(s - r) \)

2. **Rewrite the Quantities**:
- Quantity A: \( (r + s)(r - s) \)
- Quantity B: \( (r + s)(s - r) \)

3. **Factor Out Common Terms**:
Both quantities have a common factor of \( (r + s) \):
- Quantity A: \( (r + s)(r - s) \)
- Quantity B: \( (r + s)(s - r) \)

We can express the comparison as:
\[ \text{Compare } (r - s) \text{ and } (s - r) \]

4. **Analyze the Factors**:
Since \( r > s \), we know:
- \( r - s > 0 \)
- \( s - r < 0 \)

5. **Determine the Sign of Each Quantity**:
- Quantity A: \( (r + s)(r - s) \) is positive because both \( (r + s) > 0 \) (since both \( r \) and \( s \) are positive) and \( (r - s) > 0 \).
- Quantity B: \( (r + s)(s - r) \) is negative because \( (s - r) < 0 \).

6. **Conclusion**:
Since Quantity A is positive and Quantity B is negative, we conclude that:
\[ \text{Quantity A} > \text{Quantity B} \]

### Final Answer:
**Quantity A is greater than Quantity B.**

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