Using properties of determinants, show the following: `|[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3`

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

Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

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

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following |(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using the Properties of determinants, prove that following: {:|(-a^2,ab,ac),(ba,-b^2,bc),(ac,bc,-c^2)|=4a^2b^2c^2

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]]|=(ab+bc+ca)^3