Answer
$2$
Work Step by Step
$(y+1)(y^{2}-y+1)=y(y^{2}-y+1)+1(y^{2}-y+1)$
$=y^{3}-y^{2}+y+y^{2}-y+1\qquad $... combine like terms
$=y^{3}+(-y^{2}+y^{2})+(y-y)+1$
$=y^{3}+1\qquad\qquad(*)$
$(y-1)(y^{2}+y+1)=y(y^{2}+y+1)-1(y^{2}+y+1)$
$=y^{3}+y^{2}+y-y^{2}-y-1\qquad $... combine like terms
$=y^{3}+(y^{2}-y^{2})+(y-y)-1$
$=y^{3}-1\qquad\qquad(**)$
Subtract $(*) - (**)$:
$=(y^{3}+1)-(y^{3}-1)\qquad$ ... distribute/take parentheses down
=$y^{3}+1-y^{3}+1\qquad $... combine like terms
$=(y^{3}-y^{3})+(1+1)$
$=0+2$
=$2$
