Question: User: $(-w^3+8w^2-3w) -(4w^2+5w-7)=$
1. **State the problem:** Simplify the expression $$(-w^3+8w^2-3w) -(4w^2+5w-7)$$.
2. **Write the expression clearly:**
$$-w^3 + 8w^2 - 3w - (4w^2 + 5w - 7)$$
3. **Distribute the minus sign across the second parentheses:**
$$-w^3 + 8w^2 - 3w - 4w^2 - 5w + 7$$
4. **Combine like terms:**
- For $w^3$ terms: only $$-w^3$$
- For $w^2$ terms: $$8w^2 - 4w^2 = \cancel{8w^2} - \cancel{4w^2} = 4w^2$$
- For $w$ terms: $$-3w - 5w = \cancel{-3w} - \cancel{5w} = -8w$$
- Constant terms: $$7$$
5. **Write the simplified expression:**
$$-w^3 + 4w^2 - 8w + 7$$
**Final answer:** $$-w^3 + 4w^2 - 8w + 7$$