Thu gọn biểu thức: 3/4(x^3)(y^3):(-1/2)(x^2)(y^2)

a) \(\frac{3}{4}{x^3}{y^3}:\left( { - \frac{1}{2}{x^2}{y^2}} \right)\)

\[ = \left[ {\frac{3}{4}:\left( { - \frac{1}{2}} \right)} \right] \cdot \left( {{x^3}:{x^2}} \right) \cdot \left( {{y^3}:{y^2}} \right)\]

\[ =  - \frac{3}{2}xy.\]

b) \[3xy \cdot \left( {2{x^2}-3yz + {x^3}} \right)\]

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

\( = 6{x^3}y-9x{y^2}z + 3{x^4}y.\)

c) \(\left( {4{x^4} - 8{x^2}{y^2} + 12{x^5}y} \right):\left( { - 4{x^2}} \right) + 3{x^3}y\)

\( = 4{x^4}:\left( { - 4{x^2}} \right) - 8{x^2}{y^2}:\left( { - 4{x^2}} \right) + 12{x^5}y:\left( { - 4{x^2}} \right) + 3{x^3}y\)

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

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

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

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

\( =  - {x^2}{y^2} + 3x{y^2}\).