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Question

For any three number a,b and c
show that: a×(b+c)+b×(c+a)+c×(a+b)=0

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Solution

¯a×(b+c)+b×(c+a)+c×(a+b)

=a×b+a×c+b×c+b×a+c×a+c×b

=a×b+a×c+b×ca×ba×cb×c

=0=RHS

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