|[1,x,x^(2)],[1,y,y^(2)],[1,z,z^(2)]|=

|[yz,x,x^(2)],[zx,y,y^(2)],[xy,z,z^(2)]|=|[1,x^(2),x^(3)],[1,y^(2),y^(3)],[1,z^(2),z^(3)]|

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(2)]]

Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

show tha |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]| =0

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0 .

Without expanding,show that the values of the following determinants are zero: |(1,x,x^2-yz),(1,y,y^2-zx),(1,z,z^2-xy)|

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

If |(x,x^(2),1+x^(2)),(y,y^(2),1+y^(2)),(z,z^(2),1+z^(2))| where x, y, z are distinct what is |A| ?