a) $\dfrac{1}{3}x(x^2y-3xy^2+6xy+4)$
$=\dfrac{1}{3}x.x^2y-\dfrac{1}{3}x.3xy^2+\dfrac{1}{3}x.6xy+\dfrac{1}{3}x.4$
$=\dfrac{1}{3}x^3y-x^2y^2+2x^2y+\dfrac{4}{3}x$
b) $\dfrac{7}{4}x^2(xy+\dfrac{2}{3}xy-6)$
$=\dfrac{7}{4}x^2.xy+\dfrac{7}{4}x^2.\dfrac{2}{3}xy-\dfrac{7}{4}x^2.6$
$=\dfrac{7}{4}x^3y+\dfrac{7}{6}x^3y-\dfrac{21}{2}x^2$
$=\dfrac{35}{12}x^3y-\dfrac{21}{2}x^2$
c) $6x(7x^2-8x+2)$
$=42x^3-48x^2+12x$
d) $(-7xy)^2(x^2-2xy+1)$
$=49x^2y^2(x^2-2xy+1)$
$=49x^4y^2-98x^3y^3+49x^2y^2$
