Final answer:
The expression can be simplified as follows: (4t)/5 - 10t + (368t46)/546 - (5t²)/8. Therefore, the correct expression in simplified form is option (b): 4 * t² / 5 - 23 * t / 39 - 5 / 8 * t².
Step-by-step explanation:
The expression can be simplified as follows:
- Multiplying 4/5 and t gives (4/5) * t = (4t)/5
- Multiplying -10 * t gives -10t
- Combining the first two terms we get (4t)/5 - 10t
- Multiplying 8 * t46 gives 368t46
- Dividing 368t46 by 546 gives (368t46)/546
- Multiplying 5/8 and t² gives (5/8) * t² = (5t²)/8
- Combining all the terms gives the final simplified form: (4t)/5 - 10t + (368t46)/546 - (5t²)/8
Therefore, the correct expression in simplified form is option (b): 4 * t² / 5 - 23 * t / 39 - 5 / 8 * t².
The correct simplified form of the expression, taking into account the commutative property of multiplication and negative signs, is option b) 4 * t² / 5 - 23 * t / 39 - 5 / 8 * t². First, you multiply 4/5 by t and then by negative 10 * t, which gives you negative 8 * t² / 5. Next, simplify -8 * t46 / 546 by dividing -8 by 546 to get a coefficient of -23/39 for the t term. Finally, because there is no like term for t46, this term remains as it is, and you combine the t² terms to get the final simplified expression.