To simplify the expression \((4x^2 + 9x^3 + 2x) + (-6x^3 + 7x - 2)\), we will combine like terms.
- First, we can rewrite the expression by removing the parentheses:
\[ 4x^2 + 9x^3 + 2x - 6x^3 + 7x - 2 \]
- Now, let's combine the like terms:
- For \(x^3\) terms: \(9x^3 - 6x^3 = 3x^3\)
- For \(x^2\ terms: (4x^2\) (there are no other \(x^2\) terms)
- For \(x\) terms: \(2x + 7x = 9x\)
- Constant term: \(-2\) (there are no other constant terms)
- Putting it all together, we get:
\[ 3x^3 + 4x^2 + 9x - 2 \]
Thus, the simplified form of the expression is:
\[ 3x^3 + 4x^2 + 9x - 2 \]