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.

If |[b^2+c^2,ab,ac] , [ba,c^2+a^2,bc] , [ca,cb,a^2+b^2]|= a square of a determinant Delta of the third order then Delta=

Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]| is divisible by a+b+c and find the quotient.

|[bc,ca,ab],[(b+c)^(2),(c+a)^(2),(a+b)^(2)],[a^(2),b^(2)c^(2)]|

|[b^2c^2,bc,b+c] , [c^2a^2,ca,c+a] , [a^2b^2,ab,a+b]|=0

If a, b and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

The determinant |(a^2,a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab)| is divisible by

What is the determinant |(bc,a,a^(2)),(ca,b,b^(2)),(ab,c,c^(2))| equal to ?

|[b^(2)c^(2),bc,a-c],[c^(2)a^(2),ca,b-c],[a^(2)b^(2),ab,0]|=?