Show without expanding that `|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=|[1,b c, b+c],[1,c a, c+a],[1,a b, a+b]|`

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Without expanding show that : |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=|(1,bc,b+c),(1,ca,c+a),(1,ab,a+b)|

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|[1, a, a^2-b c],[1,b, b^2-c a],[1,c, c^2-a b]|=

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Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)