1. **State the problem:** Complete the square for the expression $r^2 - 6r + 9$ and rewrite it as a perfect square. 2. **Recall the formula:** To complete the square for an expression of the form $x^2 + bx + c$, find the value to add that makes it a perfect square trinomial. This value is $\left(\frac{b}{2}\right)^2$. 3. **Apply the formula:** Here, $b = -6$, so calculate: $$\left(\frac{-6}{2}\right)^2 = (-3)^2 = 9$$ 4. **Rewrite the expression:** The original expression is already $r^2 - 6r + 9$, which matches the perfect square trinomial form. 5. **Express as a perfect square:** $$r^2 - 6r + 9 = (r - 3)^2$$ **Final answer:** $(r - 3)^2$