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`

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`|[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]|=a^3+b^3+c^3-3abc`
determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca) determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca)
If a+b+c = 16, ab+bc+ca = 78 then a^3+b^3+c^3-3abc = ? | Identity Question | Algebra If a+b+c = 16, ab+bc+ca = 78 then a^3+b^3+c^3-3abc = ? | Identity Question | Algebra
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If a+b+c=5 and ab+bc+ca=10, then prove that a^3+b^3+c^3-3abc=-25. | 9 | POLYNOMIALS | MATHS | NC... If a+b+c=5 and ab+bc+ca=10, then prove that a^3+b^3+c^3-3abc=-25. | 9 | POLYNOMIALS | MATHS | NC...