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" Pruve that "|[3+z,x,y],[z-x,z,x],[x-y,...

" Pruve that "|[3+z,x,y],[z-x,z,x],[x-y,y,z]|=(x+y+zi)(x-z)^(2)

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

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

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

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

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

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

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

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z)(z+x)