= (x+y)3 - 3x2y-3xy2+z2-3xyz
=(x+y+z)[(x+y)2-(x+y)z+z2]-3x(x+y+z)
=(x+y+z)(x2+y2+z2-xy-yz-zx)
x3+y3+z2-3xyz=( x3+y3+3x2y +3xy2)-3x2y+3xy2+ z3-3xyz
= [ (x+y)3+z3 ] - [3xy(x+y) + 3xyz]
=(x+y+z)[(x+y)2 -(x+y)z+z2 ] - 3xy(x+y+z)
= (x+y+z)(x2+y2+z2+2xy-xz-yz-3xy)
=(x+y+z)(x2+y2+z2-xy-xz-yz)
x3+y3+z2-3xyz=( x3+y3+3x2y +3xy2)-3x2y+3xy2+ z3-3xyz
= [ (x+y)3+z3 ] - [3xy(x+y) + 3xyz]
=(x+y+z)[(x+y)2 -(x+y)z+z2 ] - 3xy(x+y+z)
= (x+y+z)(x2+y2+z2+2xy-xz-yz-3xy)
=(x+y+z)(x2+y2+z2-xy-xz-yz)