a) $(2x-y+2)^2$
$=(2x-y+2).(2x-y+2)$
$=[(2x-y+2).2x]-[(2x-y+2).y]+[(2x-y+2).2]$
$=[4x^2-2xy+4x]-[2xy-y^2+2y]+[4x-2y+4]$
$=4x^2-2xy+4x-2xy+y^2-2y+4x-2y+4$
$=4x^2+y^2+(-2xy-2xy)+(4x+4x)+(-2y-2y)+4$
$=4x^2+y^2-4xy+8x-4y+4$
b) $(\dfrac{xy}{2}-\dfrac{x}{3})(\dfrac{xy}{2}+\dfrac{x}{3})$
$=[(\dfrac{xy}{2}-\dfrac{x}{3}).\dfrac{xy}{2}]+[(\dfrac{xy}{2}-\dfrac{x}{3}).\dfrac{x}{3}]$
$=[\dfrac{x^2y^2}{4}-\dfrac{x^2y}{6}]+[\dfrac{x^2y}{6}-\dfrac{x^2}{9}]$
$=\dfrac{x^2y^2}{4}-\dfrac{x^2y}{6}+\dfrac{x^2y}{6}-\dfrac{x^2}{9}$
$=\dfrac{x^2y^2}{4}+(-\dfrac{x^2}{y}+\dfrac{x^2y}{6})-\dfrac{x^2}{9}$
$=\dfrac{x^2y^2}{4}-\dfrac{x^2}{9}$
