If `|a^2b^2c^2(a+1)^2(b+1)^2(c+1)^2(a-1)^2(b-1)^2(c-1)^2|=k(a-b)(b-c)(c-a),` then find the value of `kdot`

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

1,1,1a,b,ca^(2),b^(2),c^(2)]|=(a-b)(b-c)(c-a)

|[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)

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(b-1)^2,(c-1)^2)|= then

([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)