Question

show that x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx)

Answer 1

Hey! Here's your answer!

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

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

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

       = x3 + xy2 + xz2 - x2y - xyz - zx2 + yx2 + y3 + yz2- xy2 - y2z - xyz  

         + zx2 + zy2 + z3 - xyz - yz2 - xz2

       = x3 + y3 + z3 - 3xyz

       = L.H.S.

Hence Proved!

Hope this helps! :)