To solve the expression \((5x^4 + 2x^3 - 6x^2 + 2x - 8) + (2x^2)\), you simply combine like terms.

Here are the steps:

\[
(5x^4 + 2x^3 - 6x^2 + 2x - 8) + 2x^2
\]

Now, combine the \(x^2\) terms:

\[
5x^4 + 2x^3 + (-6x^2 + 2x^2) + 2x - 8
\]

This simplifies to:

\[
5x^4 + 2x^3 - 4x^2 + 2x - 8
\]

Thus, the simplified expression is:

\[
5x^4 + 2x^3 - 4x^2 + 2x - 8
\]

Would you like a deeper explanation, or do you have any further questions?

Here are 5 related questions to expand your understanding:
1. How do you combine like terms in algebraic expressions?
2. What are the steps to factor a polynomial like the one we solved?
3. How do you identify the degree of a polynomial?
4. How do you add or subtract two polynomials with different degrees?
5. How would you graph the polynomial expression we just simplified?

**Tip:** Always group similar terms (like powers of \(x\)) when simplifying polynomials.

Learn how to simplify the polynomial expression (5x^4 + 2x^3 - 6x^2 + 2x - 8) + (2x^2) by combining like terms. This problem covers essential algebraic concepts, including polynomials and like terms. Suitable for students in Grades 8-10.

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