Final answer:
The expression +3(8 + 9t) - (+2 + 4)(t² – 3t) simplifies to 6t² + 9t + 24, which is a quadratic trinomial. It has three terms, including a constant term. The simplified expression is not cubic and does not have four terms.
Step-by-step explanation:
To simplify the expression +3(8 + 9t) - (+2 + 4)(t² – 3t), let's first distribute the numbers outside the parentheses:
- 3 × 8 = 24
- 3 × 9t = 27t
- +2 × t² = +2t²
- +2 × -3t = -6t
- 4 × t² = 4t²
- 4 × -3t = -12t
Combine like terms:
- 24 (constant term)
- 27t - 6t - 12t = 9t (linear term)
- +2t² + 4t² = 6t² (quadratic term)
So the simplified expression is 6t² + 9t + 24.
Now, let's analyze the given statements based on the simplified expression:
- The simplified expression is cubic: False. It is quadratic.
- The simplified expression is a trinomial: True.
- The simplified expression has four terms: False. It has three terms.
- The simplified expression has a constant term: True.