1. **State the problem:** Simplify or factor the expression $x^2 - 30x + 225$. 2. **Recall the formula:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Apply the formula:** Here, $a=1$, $b=-30$, and $c=225$. We need two numbers that multiply to $1 \times 225 = 225$ and add to $-30$. 4. **Find the numbers:** The numbers are $-15$ and $-15$ because $-15 \times -15 = 225$ and $-15 + (-15) = -30$. 5. **Write the factorization:** $$x^2 - 30x + 225 = (x - 15)(x - 15) = (x - 15)^2$$ 6. **Final answer:** The expression factors as $$(x - 15)^2$$.