The expression you provided is a quadratic expression: \( x^2 - 15x \).

Here are a few things we can do with this expression:

### 1. **Factorization:**
We can factor out the greatest common factor, which is \( x \):

\[
x^2 - 15x = x(x - 15)
\]

### 2. **Solving the Equation:**
If you set this equal to 0 (i.e., \( x^2 - 15x = 0 \)), you can solve for \( x \):

\[
x(x - 15) = 0
\]

This gives the solutions:

\[
x = 0 \quad \text{or} \quad x = 15
\]

### 3. **Vertex Form (Completing the Square):**
To express the quadratic in vertex form, you can complete the square. 

Start with the expression \( x^2 - 15x \). To complete the square, take half of -15, square it, and add and subtract that square inside the expression:

\[
x^2 - 15x + \left( \frac{-15}{2} \right)^2 - \left( \frac{-15}{2} \right)^2
\]

\[
x^2 - 15x + \frac{225}{4} - \frac{225}{4} = \left( x - \frac{15}{2} \right)^2 - \frac{225}{4}
\]

So, the expression in vertex form is:

\[
\left( x - \frac{15}{2} \right)^2 - \frac{225}{4}
\]

Do you want more details or have any questions?

### Related Questions:
1. How do you solve a general quadratic equation?
2. What is the geometric significance of the vertex form of a quadratic?
3. Can you apply the quadratic formula to this equation?
4. How do you graph a quadratic function like \( x^2 - 15x \)?
5. What is the significance of completing the square?

**Tip:** Always check if you can factor before using more complex methods like completing the square or the quadratic formula.

Explore how to factor and solve the quadratic expression x^2 - 15x using methods like factoring and completing the square. Learn key algebraic concepts for Grades 8-10 and see step-by-step solutions to this problem.

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