1. **State the problem:** Factorize completely the expression $$x^2 (b - c) + 2x (b - c) + (b - c)$$. 2. **Identify common factors:** Notice that each term contains the factor $b - c$. 3. **Factor out the common factor:** $$x^2 (b - c) + 2x (b - c) + (b - c) = (b - c)(x^2 + 2x + 1)$$ 4. **Factor the quadratic inside the parentheses:** The quadratic $x^2 + 2x + 1$ is a perfect square trinomial because it can be written as: $$x^2 + 2x + 1 = (x + 1)^2$$ 5. **Write the complete factorization:** $$ (b - c)(x + 1)^2 $$ 6. **Conclusion:** The fully factorized form is $(b - c)(x + 1)^2$, which corresponds to option C. This means the expression is factored into the product of $(b - c)$ and the square of $(x + 1)$. **Final answer:** $(b - c)(x + 1)^2$