x^3+y^3+1-3xy
=x^3+y^3+1-3・x・y・1
=(x^3+y^3)+1^3-3xy・1
=(x+y)^3-3xy(x+y)-3xy+1^3
=(x+y)^3+1^3-3xy(x+y+1)
={(x+y+1)^3-3(x+y)^2-3(x+y)}-3xy(x+y+1)
=(x+y+1)^3-3(x+y)(x+y)-3(x+y)-3xy(x+y+1)
=(x+y+1)^3-3(x+y){(x+y)+1}-3xy(x+y+1)
=(x+y+1)(x+y+1)^2-3(x+y)(x+y+1)-3xy(x+y+1)
=(x+y+1){(x+y+1)^2-3(x+y)-3xy}
=(x+y+1){(x^2+2xy+y^2+2x+2y+1^2)-3x-3y-3xy}
=(x+y+1)(x^2+y^2+1-xy-x-y)