If 3 X + Y + Z is equal to zero show that 27 x cube + b cube + Z cube is equal to 9 x y z
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it is given that,
3x+y+z=0
LHS=27xcube+ycube+zcube _eq(1)
subtracting and adding 9xyz in equation-1
LHS=27xcube+ycube+zcube-9xyz+9xyz
=(3x+y+z)(3xsquare+ysquare+zsquare-3xy-. yz-3xz)+9xyz
=0(3xsquare+ysquare zsquare-3xy-yz-3xz)+9xyz
=0+9xyz
=9xyz=RHS
3x+y+z=0
LHS=27xcube+ycube+zcube _eq(1)
subtracting and adding 9xyz in equation-1
LHS=27xcube+ycube+zcube-9xyz+9xyz
=(3x+y+z)(3xsquare+ysquare+zsquare-3xy-. yz-3xz)+9xyz
=0(3xsquare+ysquare zsquare-3xy-yz-3xz)+9xyz
=0+9xyz
=9xyz=RHS
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