\(a)\) \(\left( {5{x^4} - 3{x^3} + {x^2}} \right):3{x^2}\)
\( = \left[ {5{x^4}:(3{x^2}}) \right] + \left[ { - 3{x^3}:(3{x^2}}) \right] \)\(+ \left[ {{x^2}:(3{x^2})} \right]\)
\( =\displaystyle {5 \over 3}{x^2} - x + {1 \over 3}\)
\(b)\) \(\left( {5x{y^2} + 9xy - {x^2}{y^2}} \right):\left( { - xy} \right)\)
\( = \left[ {5x{y^2}:\left( { - xy} \right)} \right] \)\(+ \left[ {9xy:\left( { - xy} \right)} \right]\)\( + \left[ {\left( { - {x^2}{y^2}} \right):\left( { - xy} \right)} \right] \)
\(= - 5y - 9 + xy\)
\(c)\) \(\displaystyle\left( {{x^3}{y^3} - {1 \over 2}{x^2}{y^3} - {x^3}{y^2}} \right):{1 \over 3}{x^2}{y^2}\)
\(=\displaystyle\left[ {{x^3}{y^3}:({1 \over 3}{x^2}{y^2}}) \right] + \left[ { - {1 \over 2}{x^2}{y^3}:({1 \over 3}{x^2}{y^2}}) \right] \)\(\displaystyle \)\(\displaystyle + \left[ { - {x^3}{y^2}:({1 \over 3}{x^2}{y^2}}) \right]\)
\( \displaystyle = 3xy - {3 \over 2}y - 3x \)
