Final answer:
The expression (5m⁴-5m²-6m)-(2m-5m²-m⁴) simplifies to 6m⁴ - 8m by changing the signs of the second expression and combining like terms.
Step-by-step explanation:
To simplify the expression (5m⁴-5m²-6m)-(2m-5m²-m⁴), we combine like terms by subtracting the second expression from the first. Remember, subtracting a negative is the same as adding a positive, and to subtract, you change the sign of each term in the second expression before combining like terms.
Applying these rules, we have:
5m⁴ - 5m² - 6m
- (2m - 5m² - m⁴)
= 5m⁴ - 5m² - 6m
- 2m + 5m² + m⁴
Now, combine like terms:
5m⁴ + m⁴ - 5m² + 5m² - 6m - 2m
= 6m⁴ - 8m
The expression simplifies to 6m⁴ - 8m. When simplifying expressions, we must always check our answer to make sure it is reasonable and that no term has been overlooked.