Final answer:
The sum of the polynomials is found by combining like terms, leading to a final simplified expression of 4m³ + 64m - 24n³ - 24n - 10.
Step-by-step explanation:
The sum of the polynomials 4m³ + 4m - 24n³ + 30m - 5 + 30m - 24n - 5 requires combining like terms. To combine like terms, we look for terms that have the same variable raised to the same power. In this case, we have three terms with m to the first power (4m, 30m, and 30m) and constant terms (-5 and -5).
Combining the like terms, we get:
- For m to the first power: 4m + 30m + 30m = 64m
- For the constant terms: -5 - 5 = -10
We cannot combine the terms 4m³ and -24n³ with any other terms because they are unique in their variables and exponents.
The term -24n is also unique and cannot be combined with other terms.
Thus, the final simplified sum of the polynomials is:
4m³ + 64m - 24n³ - 24n - 10