Using the properties of determinants, prove the following `|(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|`

|{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=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

Using the Properties of determinants, prove the following: {:|(1,1,1),(a,b,c),(bc,ca,ab)|=(a-b)(b-c)(c-a)

Using the properties of determinants,prove det[[1,bc,bc(b+c)1,ca,ca(c+a)1,ab,ab(a+b)]]

det[[1,bc,bc(b+c)1,ca,ca(c+a)1,ab,ab(a+b)]]=0

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

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 that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

Using the property of determinants and without expanding {:[( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )]:}=0

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0