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Without expanding the determinant, prove...

Without expanding the determinant, prove that `|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)`.

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The correct Answer is:
`=(a-b)(b-c)(c-a)`
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CHHAYA PUBLICATION-QUESTION PAPER -2018-WBJEE
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  14. The value of lim(ntooo)(1)/(n)[sec^2""(pi)/(4n)+sec^2""(2pi)/(4n)+.......

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  16. Let y(x) be a solution of (1+x^2)"" (dy)/(dx)+2xy-4x^2=0 and y(0)=-1. ...

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  20. If ar=(cos2rpi+isin2rpi)^((1)/(9)), then the value of |{:(a1,a2,a3),(a...

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  21. If Sr=|{:(2r,x,n(n+1)),(6r^2-1,y,n^2(2n+3)),(4r^3-2nr,z,n^3(n+1)):}|, ...

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