Prove-that-determinant-3-a-b-c-a-2-b-2-c-2-a-b-c-a-2-b-2-c-2-a-3-b-3-c-3-a-2-b-2-c-2-a-3-b-3-c-3-a-4-b-4-c-4-a-b-2-b-c-2-c-a-2-

Question Number 30783 by math1967 last updated on 25/Feb/18

P r o v e t h a t | \begin{matrix} 3 & a + b + c & a^{2} + b^{2} + c^{2} \\ a + b + c & a^{2} + b^{2} + c^{2} & a^{3} + b^{3} + c^{3} \\ a^{2} + b^{2} + c^{2} & a^{3} + b^{3} + c^{3} & a^{4} + b^{4} + c^{4} \end{matrix} |

= {(a - b)}^{2} {(b - c)}^{2} {(c - a)}^{2}

Answered by math1967 last updated on 27/Feb/18

F i n d | \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} | | \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} |

t h e n e x p a n d | \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} |

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