The expression \( x^2 - 54x + 324 \) is a quadratic equation. To simplify or solve it, let's check if it can be factored.

### Step 1: Factorization
We look for two numbers that multiply to 324 and add to -54. These numbers are -18 and -18 because:
\[
-18 \times -18 = 324 \quad \text{and} \quad -18 + -18 = -54
\]

Thus, the expression can be factored as:
\[
x^2 - 54x + 324 = (x - 18)(x - 18) = (x - 18)^2
\]

### Step 2: Conclusion
The expression simplifies to:
\[
(x - 18)^2
\]
This is a perfect square.

Would you like to solve this equation further or explore its properties? 

Here are five related questions:
1. How would you solve \( (x - 18)^2 = 0 \)?
2. What is the vertex form of a quadratic equation, and how does this equation relate to it?
3. What are the roots of \( x^2 - 54x + 324 = 0 \)?
4. Can you graph \( y = (x - 18)^2 \), and what does its graph look like?
5. How would you expand \( (x - 18)^2 \) back into a quadratic?

**Tip:** Perfect square quadratics have exactly one solution, called a "repeated root."

Discover how to factor and simplify the quadratic equation x² - 54x + 324. This problem demonstrates the factorization of perfect square quadratics and provides a detailed step-by-step solution. Ideal for students in Grades 8-10, covering core algebra concepts.

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