Thu gọn biểu thức:

a) \( - 3{x^2}{y^5}z:\left( {15x{y^3}} \right)\)\( = \frac{{ - 1}}{5}x{y^2}z\).

b) \(\left( { - 9{x^2}{y^3} + 6{x^3}{y^2} - 4x{y^2}} \right):3x{y^2}\)

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

\( =  - 3xy + 2{x^2} - \frac{4}{3}.\)

c) \(\frac{1}{2}xy\left( {{x^5} - {y^3}} \right) - {x^2}y\left( {\frac{1}{4}{x^4} - {y^3}} \right)\)

\( = \frac{1}{2}xy \cdot {x^5} - \frac{1}{2}xy \cdot {y^3} - {x^2}y \cdot \frac{1}{4}{x^4} + {x^2}y \cdot {y^3}\)

d) \(\left( {x + 3y} \right)\left( {x - 2y} \right) - \left( {{x^4}y - 6{x^2}{y^3}} \right):{x^2}y\)

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

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

\( = xy\).

\( = \frac{1}{2}{x^6}y - \frac{1}{2}x{y^4} - \frac{1}{4}{x^6}y + {x^2}{y^4}\)

\( = \left( {\frac{1}{2}{x^6}y - \frac{1}{4}{x^6}y} \right) - \frac{1}{2}x{y^4} + {x^2}{y^4}\)

\[ = \frac{1}{4}{x^6}y - \frac{1}{2}x{y^4} + {x^2}{y^4}\]