1.

\left| \begin{array}{ccc}{1} & {1} & {1} \\ {a^{2}} & {b^{2}} & {c^{2}} \\ {a^{3}} & {b^{3}} & {c^{3}}\end{array}\right|=(a-b)(b-c)(c-a)(a b+b c+c a)

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