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|[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]|=a^...

|[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]|=a^(3)+b^(3)+c^(3)-3abc

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Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] = a^3+b^3+c^3-3abc

[[b+c,a-b,ac+a,b-c,ba+b,c-a,c]]=3abc-a^(3)-b^(3)-c^(3)

Show that |[b+c,c+a,a+b] , [a+b,b+c,c+a] , [a,b,c]|=a^3+b^3+c^3-3abc

Prove that |(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc-a^(3)-b^(3)-c^(3)

Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c

Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc .

det[[a,b,ca-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc