`|{:(x,x^(2),1+px^(3)),(y,y^(2),1+py^(3)),(z,z^(2),1+pz^(3)):}|=(1+pxyz)(x-y)(y-z)(z-x)`

For any scalar p prove that =|x^(2)1+px^(3)yy^(2)1+py^(3)zz^(2)1+pz^(3)|=(1+pxyz)(x-y)(y-z)(z-x)

{:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that Delta=(1+pxyz)(x-y)(y-z)(z-x) .

{:|( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) |:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3))|=(x-y)(y-z)(z-x){1/x+1/y+1/z} then k=

Using properties of determinants.Prove that |xx^(2)1+px^(3)yy^(2)1+py^(3)zz^(2)1+pz^(3)|=(1+pxyz)(x-y)(y-z)(z-x) where p is any scalar.