" Q.6.Using properties of determinants prove that "|[y+z,x,y],[z+x,z,x],[x+y,y,z]|=(x+y+z)(x-z)^(2)

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)

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

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 the 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, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

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

By using properties of determinant prove that |(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

y+z,x,yz+y,z,xx+y,y,z]|=(x+y+z)(x-z)^(2)

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