1.

`|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)`

Answer» Apply `R_(2) to (R_(2) -R_(3)) " and take 4 common from "R_(2)`
Now, apply `R_(3) to R_(3)-R_(1) + 2R_(2)`


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