−35y 
4
 +40y 
3
  divided by minus, 5, y, squared−5y 
2
 .

To solve the expression:

\[
\frac{-35y^4 + 40y^3}{-5y^2}
\]

### Step-by-step solution:
1. **Split the expression:**  
   We can divide each term in the numerator by \(-5y^2\).

   \[
   \frac{-35y^4}{-5y^2} + \frac{40y^3}{-5y^2}
   \]

2. **Simplify each term individually:**
   - For the first term:  
     \[
     \frac{-35y^4}{-5y^2} = 7y^{4-2} = 7y^2
     \]

   - For the second term:  
     \[
     \frac{40y^3}{-5y^2} = -8y^{3-2} = -8y
     \]

3. **Combine the simplified terms:**

   \[
   7y^2 - 8y
   \]

### Final Answer:
\[
7y^2 - 8y
\]

---

Would you like a more detailed breakdown of any step or a related explanation?

Here are 5 related questions:
1. How do you divide polynomials step by step?
2. What are some common rules of exponents used in simplifying fractions?
3. How do you simplify algebraic expressions with multiple variables?
4. How can you factor the expression \(7y^2 - 8y\)?
5. How do negative signs affect polynomial division?

**Tip:** Always keep track of the signs when dividing negative terms—they can change the result significantly.

Discover how to divide the polynomial −35y^4 + 40y^3 by −5y^2 with this detailed step-by-step solution. This problem highlights key algebra concepts, such as polynomial division and exponent rules. Ideal for students in Grades 9-10.

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