Final answer:
The expression (2/3)x³ + 15x² + (1/6)x³ - 17x² - 16 simplifies to (5/6)x³ - 2x² - 16 by combining like terms.
Step-by-step explanation:
To simplify the expression (2/3)x³ + 15x² + (1/6)x³ - 17x² - 16, we should combine like terms. In this case, we have two cubic terms and two quadratic terms that can be combined:
- (2/3)x³ + (1/6)x³ = (4/6 + 1/6)x³ = (5/6)x³
- 15x² - 17x² = -2x²
So the expression simplifies to:
(5/6)x³ - 2x² - 16
Remember to first identify and then combine like terms, and then if necessary, simplify by common factors.