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Let's solve the given expression:

\[
u^2 + v^2 - (u - v)^2
\]

Given:
- \( u = -1 \)
- \( v = 1 \)

### Step-by-Step Solution:
1. **Substitute** the values of \( u \) and \( v \):
   \[
   (-1)^2 + (1)^2 - (-1 - 1)^2
   \]
   
2. **Simplify** the individual terms:
   \[
   (-1)^2 = 1
   \]
   \[
   (1)^2 = 1
   \]
   \[
   (-1 - 1) = -2 \quad \text{so} \quad (-2)^2 = 4
   \]
   
3. **Substitute** these results back into the expression:
   \[
   1 + 1 - 4
   \]
   
4. **Simplify the final expression**:
   \[
   2 - 4 = -2
   \]

Thus, the value of the expression is \( \boxed{-2} \).

Would you like further details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How would the expression change if both \( u \) and \( v \) were negative?
2. What happens if you expand \( (u - v)^2 \) before plugging in values?
3. Can you rewrite the expression in terms of a simpler formula involving the difference of squares?
4. How does the order of operations impact solving this type of problem?
5. What would happen if you swapped the values of \( u \) and \( v \)?

**Tip:** Always simplify expressions step-by-step to avoid calculation errors, especially when dealing with squared terms.

Evaluate the expression u^2 + v^2 - (u - v)^2 given that u = -1 and v = 1.

Learn how to evaluate the algebraic expression u^2 + v^2 - (u - v)^2 with specific values for u and v. This solution walks you through each step to help you understand how to substitute and simplify terms. Suitable for students in Grades 9-10.

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