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

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

What is the value of the determinant |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))| ?

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

The value of the determinant |{:(1,bc,a(b+c)),(1,ca,b(a+c)),(1, ab,c(a+b)):}| doesn't depend on

Without expanding prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

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

|[1,a,bc] , [1,b,ca] , [1,c,ab]|=