Express `Delta=|(2bc-a^2,c^2,b^2),(c^2,2ca-b^2,a^2),(b^2,a^2,2ab-c^2)|` as square of a determinant of hence evaluate if.

Answer

`[3abc-a^(2)-b^(3)-c^(3)]^(2)`

Explanation

The given determinants is
`|{:(a,, b,,c),(b,,c,,a),(c,,a,,b):}| xx |{:(-a,,c,,b),(-b,,a,,c),(-c,,b,,a):}|=Delta `[row by row multiplication]
Therefore
`Delta = |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}||{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|=|{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|^(2)`
`=[a(bc-a^(2))+b(ac-b^(2))+c(ab-c)^(2))]^(2)`
`=[3abc -a^(3)-b^(3)-c^(3)]^(2)`