1. **State the problem:** We need to find the expansion of the expression $ (8a + 3b)^2 $. 2. **Formula used:** The square of a binomial $ (x + y)^2 $ is given by the formula: $$ (x + y)^2 = x^2 + 2xy + y^2 $$ 3. **Apply the formula:** Here, $ x = 8a $ and $ y = 3b $. 4. **Calculate each term:** - $ x^2 = (8a)^2 = 64a^2 $ - $ y^2 = (3b)^2 = 9b^2 $ - $ 2xy = 2 \times 8a \times 3b = 48ab $ 5. **Combine all terms:** $$ (8a + 3b)^2 = 64a^2 + 48ab + 9b^2 $$ 6. **Check answer choices:** The correct answer is option D: $64a^2 + 48ab + 9b^2$. **Final answer:** $$\boxed{64a^2 + 48ab + 9b^2}$$