Add:
`x^(2) y^(2) -1, y^(2) - 1 - x^(2), 1 - x^(2) - y^(2)`

Answer

To solve the problem of adding the expressions \( x^2y^2 - 1 \), \( y^2 - 1 - x^2 \), and \( 1 - x^2 - y^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Write down the expressions**:
We have three expressions to add:
\[ (x^2y^2 - 1) + (y^2 - 1 - x^2) + (1 - x^2 - y^2) \]

2. **Combine the expressions**:
We can combine all the terms:
\[ x^2y^2 - 1 + y^2 - 1 - x^2 + 1 - x^2 - y^2 \]

3. **Group like terms**:
Now, let's group the like terms together:
- The constant terms: \(-1 - 1 + 1 = -1\)
- The \(x^2\) terms: \(-x^2 - x^2 = -2x^2\)
- The \(y^2\) terms: \(y^2 - y^2 = 0\)
- The \(x^2y^2\) term: \(x^2y^2\)

Putting it all together, we have:
\[ x^2y^2 - 2x^2 - 1 \]

4. **Final expression**:
The final result after combining all the terms is:
\[ x^2y^2 - 2x^2 - 1 \]

### Final Answer:
\[ x^2y^2 - 2x^2 - 1 \]