evaluate: `|(a+x,y,z),(x,a+y,z),(x,y,a+z)|`

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

Prove that |(y+z, x,y),(z+x, z, x),(x+y, y, z)| = (x+y+z)(x-z)^(2) .

Prove: |(z, x, y),( z^2,x^2,y^2),(z^4,x^4,y^4)|=|(x, y, z),( x^2,y^2,z^2),(x^4,y^4,z^4)|=|(x^2,y^2,z^2),(x^4,y^4,z^4),(x, y, z)|=x y z(x-y)(y-z)(z-x)(x+y+z) .

The value of |(x +y,y+z,z+x),(x,y,z),(x -y,y-z,z-x)| is euqal to

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z):}|

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)