" 8."|[1+x,1,1],[1,1+y,1],[1,1,1+z]|=xy+yz+zx+xyz

1+x,1,11,1+y,11,1,1+z]|=xy+yz+zx+xyz

1,1,1+3x1+3y,1,11,1+3z,1]|=9(3xyz+xy+yz+zx)

Using prperties of determinants, prove that : |(1,1,1+3x),(1+3y,1,1),(1,1+3z,1)| = 9(3xyz + xy + yz + zx) .

Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx)

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

Using properties of determinants prove that ((1,1,1+3x),(1+3y,1,1),(1,1+3z,1)=9(3xyz+xy+yz+zx)

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

Using Cofactors of elements of third column, evaluate Delta=|[1 , x, yz],[1, y, zx],[1, z, xy]|

solve |[1,yz,yz(y+z)],[1,zx,zx(z+x)],[1,xy,xy(x+y)]|

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)