1. **State the problem:** Simplify the expression $$(4x+7)^2$$. 2. **Formula used:** The square of a binomial $$(a+b)^2 = a^2 + 2ab + b^2$$. 3. **Apply the formula:** Here, $a=4x$ and $b=7$. 4. Calculate each term: - $a^2 = (4x)^2 = 16x^2$ - $2ab = 2 \times 4x \times 7 = 56x$ - $b^2 = 7^2 = 49$ 5. **Combine all terms:** $$16x^2 + 56x + 49$$ 6. **Final answer:** $$(4x+7)^2 = 16x^2 + 56x + 49$$