Prove that :`|[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^2, b^2, c^2], [a, b, c], [1,1,1]|`

Using properties of determinant show that : |(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^2,b^2,c^2),(a,b,c),(1,1,1)|

det[[ Prove that :,c^(2)a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),[c-1)^(2)]]=4det[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

Using the properties of determinants, prove the following |{:(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(a-1)^2,(c-1)^2):}|=4|{:(a^2,b^2,c^2),(a,b,c),(1,1,1):}|

[[a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),(c-1)^(2)]]=k[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

|[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)

Prove 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

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

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)|=0 then