`xy gt0`
`{:("Quantity A","Quantity B"),((x+y)^(2),(x-y)^(2)):}`

Answer

To solve the problem, we need to compare the two quantities given:

- Quantity A: \( (x + y)^2 \)
- Quantity B: \( (x - y)^2 \)

Given that \( xy > 0 \), this implies that both \( x \) and \( y \) are either both positive or both negative.

### Step-by-Step Solution:

1. **Expand Quantity A**:
\[ (x + y)^2 = x^2 + 2xy + y^2 \]

2. **Expand Quantity B**:
\[ (x - y)^2 = x^2 - 2xy + y^2 \]

3. **Compare the Two Quantities**:
We need to compare:
\[ x^2 + 2xy + y^2 \quad \text{(Quantity A)} \]
and
\[ x^2 - 2xy + y^2 \quad \text{(Quantity B)} \]

4. **Subtract Quantity B from Quantity A**:
\[ (x + y)^2 - (x - y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2) \]
Simplifying this gives:
\[ = 2xy + 2xy = 4xy \]

5. **Analyze the Result**:
Since \( xy > 0 \), it follows that \( 4xy > 0 \). This means:
\[ (x + y)^2 > (x - y)^2 \]

6. **Conclusion**:
Therefore, Quantity A is greater than Quantity B:
\[ \text{Quantity A} > \text{Quantity B} \]

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

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