Thu gọn biểu thức:

a) \(65{x^9}{y^5}:\left( { - 13{x^4}{y^4}} \right)\)

\( = \left[ {65:\left( { - 13} \right)} \right]\,.\,\left( {{x^9}:{x^4}} \right)\,.\,\left( {{y^5}:{y^4}} \right)\)

\( =  - 5{x^5}y\).

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

\( = \frac{2}{3}{x^2}y \cdot 3x{y^2} - \frac{2}{3}{x^2}y \cdot \frac{5}{2}y\)

\( = 2{x^3}{y^3} - \frac{5}{3}{x^2}{y^2}.\)

c) \(\left( { - 12{x^{13}}{y^{15}} + 6{x^{10}}{y^{14}}} \right):\left( { - 3{x^{10}}{y^{14}}} \right) - 4{x^3}y\)

\( = \left( { - 12{x^{13}}{y^{15}}} \right):\left( { - 3{x^{10}}{y^{14}}} \right) + \left( {6{x^{10}}{y^{14}}} \right):\left( { - 3{x^{10}}{y^{14}}} \right) - 4{x^3}y\)

\( = 4{x^3}y - 2 - 4{x^3}y\)

\( =  - 2.\)                                                                    

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

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

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

\[ =  - 2{x^2} + 3xy - {y^2}.\