" 13Using the properties of determinants,prove the following: "|[y+z,x,y],[z+x,z,x],[x+y,y,z]|=(x+y+z)

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |[2y,y-z-x,2y],[2z,2z, z-x-y],[ x-y-z, 2x,2x]|=(x+y+z)^3

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3