Question

if 3x+y+z=0 show the 27 x cube +y cube+z cube =9xyz

Answer 1

3x³+y³+z³-9xyz
x³+y³+z³-3xyz
(x+y+z) (x²+y²+z²-xy-yz-zx)
=(3x+y+z) ( (3x²+y²+z²-3x(y)-y(z)-z(3x))
=(3x+y+z) (9x²+y²+z²-(3xy)-yz-3zx)