Thực hiện phép tính:

a) \(\left( {{x^2}y + {x^3} - x{y^2} + 3} \right) + \left( {{x^3} + x{y^2} - xy - 6} \right)\).       b) \(2{x^2}{y^2}\left( {{x^3}{y^2} - {x^2}{y^3} - \frac{1}{2}{y^5}} \right)\).

c) \((3{x^3} - {x^2}y + 2xy + 3) - (3{x^3} - 2{x^2}y - xy + 3)\).         d) \(\left[ {{{\left( {3ab} \right)}^2} - 9{a^2}{b^4}} \right]:\left( {8a{b^2}} \right)\).

a) \(\left( {{x^2}y + {x^3} - x{y^2} + 3} \right) + \left( {{x^3} + x{y^2} - xy - 6} \right)\)

\( = {x^2}y + {x^3} - x{y^2} + 3 + {x^3} + x{y^2} - xy - 6\)

\[ = \left( {{x^3} + {x^3}} \right) + \left( { - x{y^2} + x{y^2}} \right) + {x^2}y - xy + (3 - 6)\]

\[ = 2{x^3} + {x^2}y - xy - 3\].

b) \(2{x^2}{y^2}\left( {{x^3}{y^2} - {x^2}{y^3} - \frac{1}{2}{y^5}} \right)\)

\( = 2{x^2}{y^2}\,.\,{x^3}{y^2} + 2{x^2}{y^2}\,.\,\left( { - {x^2}{y^3}} \right) + 2{x^2}{y^2}.\left( {\frac{{ - 1}}{2}{y^5}} \right)\)

\( = 2{x^5}{y^4} - 2{x^4}{y^5} - {x^2}{y^7}\).

c) \(\left( {3{x^3} - {x^2}y + 2xy + 3} \right) - \left( {3{x^3} - 2{x^2}y - xy + 3} \right)\)

\( = 3{x^3} - {x^2}y + 2xy + 3 - 3{x^3} + 2{x^2}y + xy - 3\)

\( = \left( {3{x^3} - 3{x^3}} \right) + \left( { - {x^2}y + 2{x^2}y} \right) + \left( {2xy + xy} \right) + (3 - 3)\)

\( = {x^2}y + 3xy\).

d) \(P = \left[ {{{\left( {3ab} \right)}^2} - 9{a^2}{b^4}} \right]:\left( {8a{b^2}} \right)\)