1. **State the problem:** Simplify the expression $-5(3p - 2n + 6m^2)$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means we multiply each term inside the parentheses by the factor outside. 3. **Apply the distributive property:** Multiply $-5$ by each term inside the parentheses: $$-5 \times 3p = -15p$$ $$-5 \times (-2n) = +10n$$ $$-5 \times 6m^2 = -30m^2$$ 4. **Write the simplified expression:** $$-15p + 10n - 30m^2$$ 5. **Explanation:** Multiplying by a negative number changes the sign of each term inside the parentheses. For the middle term, since it was negative inside, multiplying by $-5$ makes it positive. **Final answer:** $$-15p + 10n - 30m^2$$