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We are asked to find the difference between the two expressions:

\[
(5a^4 + 3a^2 - 4) - (a^4 + 2a^3 - a^2)
\]

Let's go step by step:

### Step 1: Write out the full expression
We need to subtract the second polynomial from the first, which is:

\[
(5a^4 + 3a^2 - 4) - (a^4 + 2a^3 - a^2)
\]

### Step 2: Distribute the negative sign
Apply the negative sign to the terms in the second polynomial:

\[
= 5a^4 + 3a^2 - 4 - a^4 - 2a^3 + a^2
\]

### Step 3: Combine like terms
Now, let's combine terms with the same powers of \(a\):

- Combine \(5a^4 - a^4\): 
  \[
  5a^4 - a^4 = 4a^4
  \]
  
- Combine \(-2a^3\) (no like term for \(a^3\)):

\[
-2a^3
\]

- Combine \(3a^2 + a^2\):
  \[
  3a^2 + a^2 = 4a^2
  \]

- Constant term \(-4\) (no change):
  \[
  -4
  \]

### Step 4: Final simplified expression
After combining all terms, the final result is:

\[
4a^4 - 2a^3 + 4a^2 - 4
\]

### Conclusion
The correct answer is:

\[
\boxed{d. 4a^4 - 2a^3 + 4a^2 - 4}
\]

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Would you like more details or further explanation?

Here are 5 related questions for you to consider:
1. How do you find the difference between two polynomials in general?
2. What is the significance of combining like terms when simplifying expressions?
3. How do you distribute a negative sign across a polynomial?
4. What are some tips for working with higher-degree polynomials?
5. Can this method be used to subtract polynomials of more than two terms?

**Tip:** Always remember to distribute negative signs carefully when subtracting expressions to avoid errors.

Find the difference: (5a^4 + 3a^2 - 4) - (a^4 + 2a^3 - a^2)

Learn how to find the difference between two polynomials. This detailed step-by-step solution helps you subtract (5a^4 + 3a^2 - 4) from (a^4 + 2a^3 - a^2) and combine like terms. Suitable for Grades 9-10 students studying algebra and polynomial operations.

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