1. **State the problem:** We need to find which expressions are equivalent to $$-5n^2(3n^2 - 6n)$$. 2. **Use the distributive property:** Multiply $$-5n^2$$ by each term inside the parentheses: $$-5n^2 \times 3n^2 = -15n^4$$ $$-5n^2 \times (-6n) = +30n^3$$ 3. **Combine the results:** $$-15n^4 + 30n^3$$ 4. **Check each option:** - Option 1: $$3n^3(-10 - 5n) = 3n^3 \times -10 + 3n^3 \times -5n = -30n^3 - 15n^4$$ which is $$-15n^4 - 30n^3$$, not equivalent. - Option 2: $$-15n^4 + 30n^3$$ matches our expression exactly. - Option 3: $$-15n^3(n - 2) = -15n^4 + 30n^3$$ matches our expression. - Option 4: $$(10n - 5n^2)3n^2 = 10n \times 3n^2 - 5n^2 \times 3n^2 = 30n^3 - 15n^4$$ which is $$-15n^4 + 30n^3$$ after rearranging terms, so equivalent. - Option 5: $$-15n^4 - 30n^2$$ does not match. **Final answer:** Options 2, 3, and 4 are equivalent to the original expression.