To solve this problem, we need to first simplify the expression given, and then compare the simplified result with the provided options.

The expression given is: $x^3 + 3x^2 - x + 2x^2 + 6x - 2$

Step 1: Combine like terms

• $x^3$ term: There's only one $x^3$ term, so it stays as $x^3$.
• $x^2$ terms: $3x^2 + 2x^2 = 5x^2$
• $x$ terms: $-x + 6x = 5x$
• Constant term: $-2$

Step 2: Write the simplified expression

$x^3 + 5x^2 + 5x - 2$

Step 3: Compare with the provided options

The simplified expression matches the first option: $\boxed{x^3 + 5x^2 + 5x - 2}$

This is the correct equivalent expression.

Do you want further details or have any questions?

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Here are 5 related questions you might find useful:

1. How do you expand the product of a binomial and a trinomial?
2. What are like terms, and how do you combine them?
3. How do you factor a cubic polynomial like $x^3 + 5x^2 + 5x - 2$?
4. What is the significance of the constant term in a polynomial expression?
5. How can polynomial expressions be used in real-world applications?

Tip: When simplifying expressions, always look for like terms to combine. This often makes the expression easier to understand and solve.