To factorize the expression \( 256s^3 n^4 - 196s^5 \), follow these steps:

1. **Identify the common factor**:
   - Both terms have a common factor of \( s^3 \).

   \[
   256s^3 n^4 - 196s^5 = s^3(256n^4 - 196s^2)
   \]

2. **Factor the difference of squares**:
   - The expression inside the parentheses, \( 256n^4 - 196s^2 \), is a difference of squares, which can be written as:

   \[
   256n^4 - 196s^2 = (16n^2)^2 - (14s)^2
   \]

   Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \):

   \[
   256n^4 - 196s^2 = (16n^2 - 14s)(16n^2 + 14s)
   \]

3. **Combine the factored expression**:

   \[
   256s^3 n^4 - 196s^5 = s^3(16n^2 - 14s)(16n^2 + 14s)
   \]

Thus, the fully factorized form of the expression is:

\[
\boxed{s^3(16n^2 - 14s)(16n^2 + 14s)}
\]

Would you like any details or have any questions about this factorization?

Here are some related questions you might consider:

1. How do you factor more complex polynomials?
2. What is the difference of squares formula, and why is it important?
3. Can this expression be factorized further?
4. What are the key steps in identifying common factors in an expression?
5. How does the factorization process differ for higher-degree polynomials?

**Tip**: Always look for common factors first when factorizing an expression; this can simplify the process significantly.

Learn how to factorize 256s^3 n^4 - 196s^5 with a detailed step-by-step solution. This problem covers polynomial factorization, including the difference of squares formula. Suitable for high school students in Grades 10-12.

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