[" 8.Prove that "|[(a+b)^(2),ca,bc],[ca,(b+c)^(2),ab],[bc,ab,(c+a)^(2)]|=2abc(a+b+c)^(3)],[qquad " IAICBSE "2016;" CBSE "]

Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b+c)^3

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

Prove that (a+b+c)(ab+bc+ca)>9abc

Prove that : |{:(b^(2)c^(2),bc, b+c),(c^(2)a^(2),ca, c+a),(a^(2)b^(2),ab, a+b):}|=0

Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

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 [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c^2 .

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Using the properties of determinants, prove the following |{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}|=2abc(a+b+c)^3