Evaluate the following: ` |[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]|

Find the value of det[[1,a,a^(2)-bc1,b,b^(2)-ac1,c,c^(2)-ab]]

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0

det[[1,a,a^(2)+bc1,b,b^(2)+ac1,c,c^(2)+ab]] is equal to

|[(1)/(a),a^(2),bc],[(1)/(b),b^(2),ca],[(1)/(c),c^(2),ab]|=0

|(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|=........

The value of the determinant |{:(1,a, a^(2)-bc),(1, b, b^(2)-ca),(1, c, c^(2)-ab):}| is…..

The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)| , is