1. Stating the problem: We need to verify if the factorizations given are correct. 2. For part B, the original expression is $$27n + 36 - 18n^3$$ and the proposed factorization is $$3n(9 + 12 - 6n)$$. 3. Let's expand the proposed factorization: $$3n \times 9 = 27n$$ $$3n \times 12 = 36n$$ $$3n \times (-6n) = -18n^2$$ 4. The expanded form is $$27n + 36n - 18n^2$$, which is not equal to the original expression $$27n + 36 - 18n^3$$. 5. Therefore, the factorization for part B is incorrect. 6. For part D, the original expression is $$25xy + 15x^2 - 30x^2y^2$$ and the proposed factorization is $$5xy(5 + 3x - 6xy)$$. 7. Let's expand the proposed factorization: $$5xy \times 5 = 25xy$$ $$5xy \times 3x = 15x^2y$$ $$5xy \times (-6xy) = -30x^2y^2$$ 8. The expanded form is $$25xy + 15x^2y - 30x^2y^2$$, which is not equal to the original expression $$25xy + 15x^2 - 30x^2y^2$$. 9. Therefore, the factorization for part D is incorrect. Final answer: Both factorizations are incorrect.