Show that:left| begin{matrix} 1 & { a }^{ 2 } & { a }^{ 3 } 1 & { b }^{ 2 } & { b }^{ 3 } 1 & { c }^{ 2 } & { c }^{ 3 } end{matrix} right| =(a-b)(b-c)( c-a)(ab+bc+ca)
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Prove that begin{vmatrix} 1 & 1 & 1 { a }^{ 2 } & { b }^{ 2 } & { c }^{ 2 } { a }^{ 3 } & { b }^{ 3 } & { c }^{ 3 } end{vmatrix}=(a-b)(b-c)(c-a)(ab+bc+ ca)
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