The LCM of `xy+yz+zx+y^2` and `x^2+xy+yz+zx`

Show that |[yz-x^2, zx-y^2, xy-y^2] , [zx-y^2, xy-z^2, yz-x^2] , [xy-z^2, yz-x^2, zx-y^2]|= |[r^2, u^2, u^2] , [u^2, r^2, u^2] , [u^2, u^2, r^2]| where r^2 = x^2+y^2+z^2 and u^2= xy+yz+zx

Find the sum of the following algebraic expressions : 4xy - 3yz + 2zx , 2xy - yz - zx , - xy + 5yz + 6zx

Obtain the product of xy,yz, zx

If x+y+z=0,x^2+y^2+z^2=60, find xy + yz + zx

If x+y+z=0,x^2+y^2+z^2=60, find xy + yz + zx

What should be added to xy+yz+zx to get -xy-yz-zx

xquad x ^ (2), y2yquad y ^ (2), 2xz, z ^ (2), xy] | = (xy) (yz) (zx) (xy + yz + 2x)