Final answer:
The multiplication of (-1) times itself three times and then times (2m + 1) results in -(2m + 1), as the product of an odd number of negative numbers is negative. Since the specific value of m is not given, the correct answer is 'None of the above'.
Step-by-step explanation:
The question involves multiplication and understanding the rules for multiplying integers with different signs. To determine the product of (-1) × (-1) × (-1) × (2m + 1), where m is a natural number, we need to understand the following multiplication rules:
- When two negative numbers multiply, the answer has a positive sign, e.g., (-2) × (-3) = +6.
- However, when you multiply an odd number of negative numbers, the result is negative, e.g., (-1) × (-1) × (-1) = -1.
So, multiplying the three negative ones gives us -1, and then we need to multiply that by (2m + 1). Since we do not have a specific value for m, the result is simply -1 × (2m + 1), which is -(2m + 1). Because m is a natural number, (2m + 1) is also a natural number, and thus the result must be negative.
None of the given options A, B, C, or D is simply -(2m + 1) without a specific value for m, so the correct answer is None of the above.