|[a,b,c],[b,c,a],[c,a,b]|

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Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],[b,c,a],[c,a,b]]

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

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

|(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=

Prove that : |[a+b+c,-c,-b],[-c, a+b+c, -a],[-b,-a,a+b+c]|= 2(a+b)(b+c)(c+a)

Prove that |[a+b+c, -c, -b],[-c, a+b+c, -a],[-b, -a, a+b+c]|=2(a+b)(b+c)(c+a)

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

Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(a+b-c)(b+c-a)(c+a-b)

Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)

Prove that: |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)