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.

You made an error while substituting into $(a^2 + ab + b^2)$ .
