Show that `|[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|=abc(a-b)(b-c)(c-a)`

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Show that `|[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|=abc(a-b)(b-c)(c-a)` 0:03:05

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Prove that `(a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)`. 0:03:38

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If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc ?

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a b c are all non zero and a+b+c=0 prove that a^2/bc+b^2/ac+c^2/ab=3 abc are non zero and a+b+c=0