1. **State the problem:** Simplify or factor the quadratic expression $4x^2 + 28x + 49$. 2. **Recall the formula:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for two binomials $(mx + n)(px + q)$ such that $mp = a$, $nq = c$, and $mq + np = b$. 3. **Identify coefficients:** Here, $a = 4$, $b = 28$, and $c = 49$. 4. **Check if the quadratic is a perfect square:** Since $4x^2 = (2x)^2$ and $49 = 7^2$, check if $28x = 2 \times 2x \times 7$. 5. Calculate $2 \times 2x \times 7 = 28x$, which matches the middle term. 6. **Therefore, the quadratic is a perfect square trinomial:** $$4x^2 + 28x + 49 = (2x + 7)^2$$ 7. **Final answer:** $$\boxed{(2x + 7)^2}$$