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.