Let's simplify the given expression:

\[
\frac{2 - 7(-5 + h)^2 - 2 - 7(-5)^2}{h}
\]

### Step-by-Step Simplification

1. **Evaluate the squares and constants:**

   The expression inside the square, \((-5 + h)^2\), expands to:

   \[
   (-5 + h)^2 = (-5)^2 + 2(-5)(h) + h^2 = 25 - 10h + h^2
   \]

   Thus:

   \[
   -7(-5 + h)^2 = -7(25 - 10h + h^2) = -175 + 70h - 7h^2
   \]

2. **Substitute these results into the original expression:**

   \[
   \frac{2 - (-175 + 70h - 7h^2) - 2 - 7 \cdot 25}{h}
   \]

   Simplify the terms:

   \[
   = \frac{2 + 175 - 70h + 7h^2 - 2 - 175}{h}
   \]

3. **Combine like terms:**

   \[
   = \frac{0 + 7h^2 - 70h}{h}
   \]

   Simplify further by factoring out \(h\):

   \[
   = \frac{h(7h - 70)}{h}
   \]

4. **Cancel the \(h\) in the numerator and denominator:**

   Since \(h \neq 0\), we can cancel:

   \[
   = 7h - 70
   \]

### Final Answer

The simplified form of the expression is:

\[
7h - 70
\]

Would you like further details, or do you have any questions about this solution?

### Related Questions

1. How do you expand binomials using the FOIL method?
2. What are some common techniques for factoring quadratic expressions?
3. How does the limit definition of a derivative relate to the simplified expression above?
4. What are common mistakes when simplifying algebraic fractions?
5. How can we apply these algebraic techniques to solve real-world problems?

### Tip

Always double-check your algebraic manipulations, especially when expanding or factoring expressions, to avoid minor errors that can lead to incorrect results.

Learn how to simplify the algebraic expression (2−7(−5+h)^2−2−7(−5)^2)/h with a detailed step-by-step solution. This problem involves polynomial expansion, algebraic simplification, and the application of the difference quotient. Suitable for students in Grades 10-12.

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