The expression \(100 - x^2\) is a quadratic expression. It can be analyzed and manipulated in various ways depending on what you need to do with it. Here are a few common operations and interpretations:

1. **Factoring**:
The expression can be factored using the difference of squares formula:
\[
100 - x^2 = (10)^2 - (x)^2 = (10 - x)(10 + x)
\]

2. **Graphing**:
The graph of the function \(f(x) = 100 - x^2\) is a downward-opening parabola with its vertex at \((0, 100)\). The parabola intersects the x-axis at \(x = -10\) and \(x = 10\).

3. **Roots**:
To find the roots of the equation \(100 - x^2 = 0\), set the expression equal to zero and solve for \(x\):
\[
100 - x^2 = 0 \implies x^2 = 100 \implies x = \pm 10
\]
So, the roots are \(x = 10\) and \(x = -10\).

4. **Vertex**:
The vertex form of a quadratic function \(ax^2 + bx + c\) can be found by completing the square or using the vertex formula \(x = -\frac{b}{2a}\). For \(f(x) = 100 - x^2\), the vertex is at \((0, 100)\).

5. **Range and Domain**:
- The domain of \(f(x) = 100 - x^2\) is all real numbers, \(\mathbb{R}\).
- The range of \(f(x)\) is all real numbers less than or equal to 100, i.e., \((-\infty, 100]\).

6. **Derivative**:
The derivative of \(f(x) = 100 - x^2\) with respect to \(x\) is:
\[
f'(x) = -2x
\]
This tells us the slope of the tangent line to the curve at any point \(x\).

7. **Integral**:
The indefinite integral of \(100 - x^2\) with respect to \(x\) is:
\[
\int (100 - x^2) \, dx = 100x - \frac{x^3}{3} + C
\]
where \(C\) is the constant of integration.

If you have a specific question or need a particular type of analysis, please let me know!