$a)(x^2-2x+3)($$\dfrac{1}{2}x$$-5)$
$=x^2.($$\dfrac{1}{2}x$$-5)-2x.($$\dfrac{1}{2}x$$-5)+3.($$\dfrac{1}{2}x$$-5)$
$=$$\dfrac{1}{2}x^3$$-5x^2-x^2+10x+$$\dfrac{3}{2}x$$-15$
$=$$\dfrac{1}{2}x^3$$-6x^2+$$\dfrac{23}{2}x$$-15$
$b)(x^2-2xy+y^2)(x-y)$
$=x^2.(x-y)-2xy.(x-y)+y^2.(x-y)$
$=x^3-x^2y-2x^2y+2xy^2+xy^2-y^3$
$=x^3-3x^2y+3xy^2-y^3$
@Nobitao@