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