1. **State the problem:** Expand and simplify the expression $ (6x + 7)^2 $. 2. **Formula used:** The square of a binomial $ (a + b)^2 = a^2 + 2ab + b^2 $. 3. **Apply the formula:** Here, $a = 6x$ and $b = 7$. So, $$ (6x + 7)^2 = (6x)^2 + 2 \times (6x) \times 7 + 7^2 $$ 4. **Calculate each term:** $$ (6x)^2 = 36x^2 $$ $$ 2 \times (6x) \times 7 = 84x $$ $$ 7^2 = 49 $$ 5. **Combine all terms:** $$ 36x^2 + 84x + 49 $$ 6. **Final answer:** $$ (6x + 7)^2 = 36x^2 + 84x + 49 $$