Without expanding show that `|[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2b^2,a b ,a+b]|=0`

Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+b|=0 .

Without expanding prove that, |{:(b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b^2,ab,a+b):}|=0

Without expanding determinant show that |(b+c,bc,b^2c^2),(c+a,ca,c^2a^2),(a+b,ab,a^2b^2\)|=0

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

Using the property of determinants and without expanding, prove that: |[-a^2,a b, a c],[ b a, -b^2,b c],[c a, c b,-c^2]|=4a^2b^2c^2

Without expanding show that : |(bc,a,a^2),(ca,b,b^2),(ab,c,c^2)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

Show without expanding that |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=|[1,b c, b+c],[1,c a, c+a],[1,a b, a+b]|

Show without expanding at any stage that: |[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

Show without expanding at any stage that: [a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|