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The problem asks which of the given expressions is the square of \(-x - y\). Let's calculate the square of \(-x - y\) step-by-step.

### Step 1: Expand the square of \(-x - y\)
\[
(-x - y)^2 = (-x)^2 + 2(-x)(-y) + (-y)^2
\]

### Step 2: Simplify each term
1. \((-x)^2 = x^2\)
2. \(2(-x)(-y) = 2xy\)
3. \((-y)^2 = y^2\)

### Step 3: Combine the terms
\[
(-x - y)^2 = x^2 + 2xy + y^2
\]

This matches option **(d)**: \(x^2 + 2xy + y^2\).

### Answer: 
The correct answer is **(d)**.

Would you like any further details or explanation?

Here are five related questions to explore further:
1. How do you expand binomials using the distributive property?
2. What happens when you square a binomial with negative terms?
3. Can you explain why the middle term in the expansion involves \(xy\)?
4. How do you factor the expression \(x^2 + 2xy + y^2\)?
5. What is the result of squaring a binomial like \(x + y\)?

**Tip:** Remember, the square of a binomial always results in three terms: two squares and a middle term involving both variables.

Which one of the following is the square of -x - y?

Learn how to find the square of -x - y and choose the correct expression. This problem demonstrates key algebraic principles, including binomial expansion and quadratic expressions. Suitable for students in Grades 8-10.

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