1. **State the problem:** Factor the quadratic expression $x^2 - 10x + 25$. 2. **Recall the factoring formula:** For a quadratic expression $ax^2 + bx + c$, if it can be factored as $(x - p)^2$, then $p$ satisfies $p^2 = c$ and $-2p = b$. 3. **Identify coefficients:** Here, $a = 1$, $b = -10$, and $c = 25$. 4. **Check if it is a perfect square trinomial:** Calculate $p$ such that $p^2 = 25$ gives $p = 5$. 5. **Verify the middle term:** $-2p = -2 \times 5 = -10$, which matches $b$. 6. **Write the factored form:** Therefore, the expression factors as $$ (x - 5)^2 $$. 7. **Final answer:** The factorization of $x^2 - 10x + 25$ is $$(x - 5)^2$$.