Final answer:
The expression (-4x² + 9x³ + 2x) + (-6x³ + 7x - 2) simplifies to 3x³ - 4x² + 9x - 2 by combining like terms.
Step-by-step explanation:
To simplify the expression (-4x² + 9x³ + 2x) + (-6x³ + 7x - 2), we need to combine like terms, which means adding or subtracting the coefficients of terms with the same variables raised to the same power. We group the terms with x³, the terms with x², and terms with x separately:
9x³ - 6x³ = 3x³
-4x² + 0x² = -4x² (since there's no x² term in the second binomial)
2x + 7x = 9x
And for the constant terms:
0 - 2 = -2
Now, combine all the simplified terms:
3x³ - 4x² + 9x - 2
This is the simplified version of the given expression.