Question

factorize x^3+y^3+z^3-3xyz = [(x+y+z) {(x-y)^2+(y-z)^2+(z-x)^2}]​

Answer 1

Answer:

Explanation:

We have, L.H.S.=x^ 3  + y  ^3  + z^  3  − 3xyz

=( x + y + z)( x^2  + y^2  +z^2  − xy − yz − zx)           [by poynomial identity]

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

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

Hence proved.