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|[b+c,a-c,a-b],[b-c,c+a,b-a],[c-b,c-a,a+...

|[b+c,a-c,a-b],[b-c,c+a,b-a],[c-b,c-a,a+b]|=8abc

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det[[b+c,a-c,a-bb-c,c+a,b-ac-b,c-a,a+b]]=8abc

if |(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=k(abc) .Then k is:

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|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

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Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

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