Question: User: $(f^3-5f+25) -(4f^2-12f+9)=$
1. **State the problem:** Simplify the expression $$ (f^3 - 5f + 25) - (4f^2 - 12f + 9) $$.
2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each term in the second polynomial:
$$ f^3 - 5f + 25 - 4f^2 + 12f - 9 $$
3. **Group like terms:** Group terms with the same powers of $f$:
$$ f^3 - 4f^2 + (-5f + 12f) + (25 - 9) $$
4. **Simplify each group:**
- Combine the $f$ terms: $$ -5f + 12f = 7f $$
- Combine the constants: $$ 25 - 9 = 16 $$
5. **Write the simplified expression:**
$$ f^3 - 4f^2 + 7f + 16 $$
**Final answer:** $$ f^3 - 4f^2 + 7f + 16 $$