Without expanding, show that the value of each of the determinants is zero: `|a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b|`

Without expanding,show that the value of each of the determinants is zero: det[[a+b,2a+b,3a+b2a+b,3a+b,4a+b4a+b,5a+b,6a+b]]

Without expanding, show that the value of each of the determinants is zero: |1/a a^2b c a/bb^2a c a/cc^2a b|

Without expanding, show that the value of each of the determinants is zero: |1/a a^2 bc 1/b b^2 ac 1/c c^2 ab|

Without expanding, show that the value of each of the following determinants is zero: |1//a , a^2b c1//bb^2a c1//cc^2a b| (ii) |a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b| (iii) |1a a^2 1bb^2 1cc^2\ \ \ -b c-a c-a b|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding,show that the values of the following determinants are zero: |(a,b,c),(2,5,7),(a+4,b+10,c+14)|

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |a b c b c a c a b| .

Without expanding,show that the values of the following determinants are zero: |(x,y,z),(x+3a,y+3b,z+3c),(a,b,c)|

Without expanding show that the following determinants vanish |(4,a,b+c),(4,b,c+a),(4,c,a+b)|