1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 4x + 4$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored using the formula for a perfect square trinomial: $$a^2 + 2ab + b^2 = (a + b)^2$$ 3. **Identify terms:** Here, $x^2$ is $a^2$, $4x$ is $2ab$, and $4$ is $b^2$. 4. **Check if it fits the perfect square pattern:** - $a = x$ - $b = 2$ - $2ab = 2 \times x \times 2 = 4x$ which matches the middle term. 5. **Write the factorization:** $$x^2 + 4x + 4 = (x + 2)^2$$ 6. **Explanation:** This means the quadratic is a perfect square and can be expressed as the square of a binomial. **Final answer:** $$(x + 2)^2$$