1. **State the problem:** Simplify the expression $-(4x^3 + 3x^2 - 3x + 12)$. 2. **Formula and rule:** When a negative sign is placed before parentheses, it means to distribute the negative sign to each term inside the parentheses. This is equivalent to multiplying each term by $-1$. 3. **Apply the rule:** Multiply each term inside the parentheses by $-1$: $$-(4x^3) = -4x^3$$ $$-(3x^2) = -3x^2$$ $$-(-3x) = +3x$$ $$-(12) = -12$$ 4. **Write the simplified expression:** $$-4x^3 - 3x^2 + 3x - 12$$ 5. **Explanation:** Distributing the negative sign changes the sign of each term inside the parentheses. Negative times positive is negative, and negative times negative is positive. **Final answer:** $$-4x^3 - 3x^2 + 3x - 12$$