Final answer:
The polynomial simplifies to 6t³ − t⁴ − 4t² + 12t.
Step-by-step explanation:
When simplifying the given polynomial t³(8+9t)−(t²+4)(t²−3t), we can start by distributing the t³ to the terms inside the parentheses. This gives us 8t³ + 9t⁴ − t²(t² − 3t) − 4(t² − 3t). Next, we can simplify each term by combining like terms and simplifying the exponents. After simplifying, we get the final result 9t⁴ − 3t³ − 3t⁴ + 9t³ − 4t² + 12t. So, the statement that is true about the result is that the polynomial simplifies to 6t³ − t⁴ − 4t² + 12t.