1. **State the problem:** Factor the expression $$x^2 + 2x + 1 - y^2$$. 2. **Recognize the structure:** The expression can be seen as a difference of squares because $$x^2 + 2x + 1$$ is a perfect square trinomial. 3. **Rewrite the perfect square:** $$x^2 + 2x + 1 = (x+1)^2$$. 4. **Rewrite the expression:** $$ (x+1)^2 - y^2 $$. 5. **Use the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$. 6. **Apply the formula:** Here, $$a = (x+1)$$ and $$b = y$$, so $$ (x+1)^2 - y^2 = ((x+1) - y)((x+1) + y) $$. 7. **Final factored form:** $$ (x + 1 - y)(x + 1 + y) $$. This is the fully factored form of the given expression.