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The question asks to simplify the expression: 

\[
(2x^4 - 8x^2 + 4) + (2x^2 - 2)
\]

Let me walk through the solution step by step:

### Step 1: Write the expression.
We need to simplify:
\[
(2x^4 - 8x^2 + 4) + (2x^2 - 2)
\]

### Step 2: Combine like terms.
Group the terms with similar powers of \( x \):
- \( 2x^4 \) remains unchanged as it has no like terms.
- Combine the \( x^2 \) terms: \( -8x^2 + 2x^2 = -6x^2 \).
- Combine the constant terms: \( 4 - 2 = 2 \).

Thus, the simplified expression is:
\[
2x^4 - 6x^2 + 2
\]

### Step 3: Compare with the answer choices.
Looking at the provided answer options:

- **a)** \( (x^2 - 6)(2x^2 - 2) \)
- **b)** \( (x^2 - 2)(x^2 - 1) \)
- **c)** \( (x^2 - 2)(2x^2 + 2) \)
- **d)** \( (2x^2 - 4)(x^2 - 1) \)

The simplified expression \( 2x^4 - 6x^2 + 2 \) matches option **c**, since when factored out, it resembles \( (x^2 - 2)(2x^2 + 2) \).

### Final Answer:
The correct answer is **c**.

---

Do you want any details or have further questions? Here are 5 related questions you can explore:

1. How do you factor expressions like \( 2x^4 - 6x^2 + 2 \)?
2. What is the significance of like terms in simplifying polynomials?
3. How can you verify a simplified expression matches a factored form?
4. How does factoring help in solving polynomial equations?
5. What role does substitution play in checking solutions to polynomial equations?

**Tip:** Always check for common factors before trying to factor more complex polynomials; it simplifies the process significantly.

Simplify the expression: (2x^4 - 8x^2 + 4) + (2x^2 - 2)

Learn how to simplify and factor the polynomial expression (2x^4 - 8x^2 + 4) + (2x^2 - 2) with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomial simplification, factoring, and the use of the distributive property. Suitable for students in Grades 9-10.

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