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.