Thu gọn biểu thức: 65(x^9)(y^5):( - 13(x^4)(y^4))

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

\( =  - 5{x^5}y\).

b) \(x\left( {x - y} \right) + y\left( {x + y} \right)\)

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

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

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

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

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

\[ =  - 2{x^2} + 3xy - {y^2}.\]

d) \(\left( {12{x^3}y - 12{x^2}{y^2}} \right):3xy - \left( {x - 1} \right)\left( {x + xy} \right)\)

\( = 4{x^2} - 4xy - \left( {{x^2} + {x^2}y - x - xy} \right)\)

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

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