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

The value of det[[a,b,ca^(2),b^(2),c^(2)bc,ca,ab]] equal to

Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove the following : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=|{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a) .

Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2),c^(2)),( bc,ca,ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a)

Prove that: 1/(bc+ca+ab)|[a, b, c],[a^2, b^2, c^2], [bc, ca, ab]|=(b-c),(c-a),(a-b)

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,ca,ab)|=(a-b)(b-c)(c-a)(ab+bc+ca)

If a,b, and c are non - zero real numbers, then Delta=|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)b^(2),ab,a+b)| is equal to a) abc b) a^(2)b^(2)c^(2) c)bc+ca+ab d)None of these

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

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.