1. **Find** $(2x + 9)^2$. This means we need to square the binomial. 2. Use the formula for squaring a binomial: $$(a + b)^2 = a^2 + 2ab + b^2$$ 3. Here, $a = 2x$ and $b = 9$. 4. Calculate each term: - $a^2 = (2x)^2 = 4x^2$ - $2ab = 2 \times 2x \times 9 = 36x$ - $b^2 = 9^2 = 81$ 5. Combine the terms: $$4x^2 + 36x + 81$$ 6. **Answer for the first problem:** Option D. 7. **Find** $(6m + 11n)^2$. Again, square the binomial. 8. Use the same formula: $$(a + b)^2 = a^2 + 2ab + b^2$$ 9. Here, $a = 6m$ and $b = 11n$. 10. Calculate each term: - $a^2 = (6m)^2 = 36m^2$ - $2ab = 2 \times 6m \times 11n = 132mn$ - $b^2 = (11n)^2 = 121n^2$ 11. Combine the terms: $$36m^2 + 132mn + 121n^2$$ 12. **Answer for the second problem:** Option D.