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hI... how to proof (AXB).(CXD)+(BXC).(AXD)+(CXA).(BXD)=0
Hm. Are you trying to prove that without any information at all about A, B, C, and D?
Distribute terms AC+AD+BC+BD+AB+BD+AC+CD+BC+CD+AB+AD=0
At this point, it depends on the values or restrictions on A, B, C, and D
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4 hours ago