1. **State the problem:** Simplify the expression $$(\alpha - \beta)^2 + 4(\alpha - \beta) + 4$$. 2. **Recall the formula:** The expression resembles a perfect square trinomial of the form $$x^2 + 2ax + a^2 = (x + a)^2$$. 3. **Identify terms:** Let $$x = (\alpha - \beta)$$ and $$a = 2$$. 4. **Rewrite the expression:** $$ (\alpha - \beta)^2 + 4(\alpha - \beta) + 4 = x^2 + 2 \cdot 2 \cdot x + 2^2 $$ 5. **Recognize perfect square:** This matches the pattern $$x^2 + 2ax + a^2 = (x + a)^2$$. 6. **Simplify:** $$ (\alpha - \beta + 2)^2 $$ **Final answer:** $$(\alpha - \beta + 2)^2$$.