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

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]|

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

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

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

Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(c,c^2,ab)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

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|

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

Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

If a^(2) + b^(2) + c^(3) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1