$D=(x-2)^3-(y-3)^2+(x-y)(x^2+xy+y^2)-(x+y)^3$
$=(x^3-6x^2+12x-8)-(y^2-6y+9)+(x^3-y^3)-(x^3+3x^2y+3xy^2+y^3)$
$=x^3-6x^2+12x-8-y^2+6y-9+x^3-y^3-x^3-3x^2y-3xy^2-y^3$
$=x^3-3x^2y-3xy^2-2y^3-6x^2-y^2+12x+6y-17$
$=1^3-3.1^2 . \dfrac{1}{2}-3.1 . (\dfrac{1}{2})^2-2. (\dfrac{1}{2})^3-6 . 1^2- (\dfrac{1}{2})^2+12.1+6 . \dfrac{1}{2} -17$
$=1-\dfrac{3}{2}-\dfrac{3}{4}-\dfrac{1}{4}-6-\dfrac{1}{4}+12+3-17$
$=(1-6+12+3-17)+(-\dfrac{3}{2}-\dfrac{3}{4}-\dfrac{1}{4}-\dfrac{1}{4})$
$=-7-\dfrac{11}{4}$
$=-\dfrac{39}{4}$
