$*)A=xy^2.1/2.x^2.y-2x^2.y^2-1/2.x^3.y^3+3xy.(-2xy)+x$
$=1/2.x^3.y^3-2x^2.y^2-1/2x^3.y^3-6x^2.y^2+x$
$=(1/2x^3.y^3-1/2x^3.y^3)-(2x^2.y^2+6x^2.y^2)+x$
$=-8x^2.y^2+x$
$*)B=2x^2.y.4y-2x^3.y^4-1/2x^3.y^3+2x^3.y^4-xy$
$=8x^2.y^2-2x^3.y^4-1/2x^3.y^3+2x^3.y^4-xy$
$(-2x^3.y^4+2x^3.y^4)+8x^2.y^2-1/2x^3.y^3-xy$
$=8x^2.y^2-1/2x^3.y^3-xy$
$*)A+B=-8x^2.y^2+x+8x^2.y^2-1/2x^3.y^3-xy$
$=(-8x^2.y^2+8x^2.y^2)+x-1/2x^3.y^3-xy$
$=x-1/2x^3.y^3-xy$
