Please explain where the $2x$ came from in this cubic identity: The question is to factorize the difference of cube identity $(x + 1)^3 - y^3$ I obviously want to put it in the form of $(a - b)(a^2 + ab + b^2)$ My working out: $(a - b) = (x + 1) - (y) = (x + 1 - y)$ $(a^2 + ab + b^2) = (x^2 + 1) + (x + 1)(y) + (y^2) = (x^2 + 1 + xy + y + y^2) $ Therefore, $=(x + 1 - y)(x^2 + 1 + xy + y + y^2)$ Much to my dismay, the correct answer is.. $=(x + 1 - y) (x^2 + 2x + 1 + xy + y + y2)$ Any help would be much appreciated, regards.

Note that $$a^2+ab+b^2={\mathbf{\color{red}{(x+1)^2}}}+(x+1)y+y^2$$ and $(x+1)^2\
eq x^2+1$.