x³+y³+z³-3xyz= ½(x+y+z) (2x²+2y²+2z²-2xy-2yz-2zx)
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Step-by-step explanation:
x³+y³+z³-3xyz= ½(x+y+z) (2x²+2y²+2z²-2xy-2yz-2zx)
RHS= ½(x+y+z) (2x²+2y²+2z²-2xy-2yz-2zx)
= 1/2{(X) (2x²+2y²+2z²-2xy-2yz-2zx) + (y) (2x²+2y²+2z²-2xy-2yz-2zx) + (z) (2x²+2y²+2z²-2xy-2yz-2zx) }
= 1/2{2 x³+2xy²+2xz²-2x²y-2xyz-2zx²+2x²y + 2y³+2z²y -2xy²+2y²z-2xyz+ 2x²z+2y²z+2z³-2xyz- 2yz²- 2xz²}
= 1/2(2x³+2y³+2z³-6xyz)
= x³+y³+z³-3xyz
=LHS
SO LHS = RHS
Hence proved
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