1. The problem is to understand why 1's complement and 2's complement methods were not used to solve a particular problem. 2. 1's complement and 2's complement are binary number representations used primarily for encoding signed integers in computer systems. 3. 1's complement inverts all bits of a binary number, while 2's complement inverts all bits and adds 1. 4. These methods are useful for binary arithmetic and handling negative numbers in digital electronics and computer science. 5. If the problem is algebraic or involves other mathematical operations not related to binary arithmetic or signed integer representation, these complements are not applicable. 6. Therefore, the reason for not using 1's complement and 2's complement is that the problem context does not involve binary signed number operations but likely involves standard algebraic or arithmetic methods. 7. In summary, 1's and 2's complement are specific tools for binary signed number manipulation, not general mathematical problem-solving techniques.