Question

Verify that: x^3+y^3+z^3-3xyz=1/2 (x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2] Verify by solving RHS​

Answer 1

Answer:

taking RHS

1/2(x+y+z) [(x-y) ^2+(y-z) ^2+(z-x) ^2)]

=1/2(x+y+z) (x^2+y ^2-2xy+y^2+2yz+z^2+x^2-2zx)

=1/2(x+y+z) (2x ^2+2y^2+22Xy -2Zx -2yz)

=1/2 (x+y+z) ×2(x ^2+Y ^2+Z ^2-xy-yz-zx)

1/2and 2 will cancel

hence the formula will formed...