1. **State the problem:** Factor the quadratic expression $$x^2 - 10x + 25$$. 2. **Recall the factoring formula:** A quadratic expression of the form $$x^2 + bx + c$$ can be factored as $$(x - p)(x - q)$$ where $$p$$ and $$q$$ satisfy $$p + q = b$$ and $$pq = c$$. 3. **Identify coefficients:** Here, $$b = -10$$ and $$c = 25$$. 4. **Find two numbers that add to $$-10$$ and multiply to $$25$$:** These numbers are $$-5$$ and $$-5$$ because $$-5 + (-5) = -10$$ and $$-5 \times -5 = 25$$. 5. **Write the factored form:** $$ x^2 - 10x + 25 = (x - 5)(x - 5) = (x - 5)^2 $$ 6. **Explain:** This is a perfect square trinomial because it can be written as the square of a binomial. **Final answer:** $$\boxed{(x - 5)^2}$$