\(\begin{array}{l}
a)\,\,\left( { - 2{x^2} + \frac{3}{4}{y^2} - 7xy} \right).4x{y^2}\\
= - 2{x^2}.4x{y^2} + \frac{3}{4}{y^2}.4x{y^2} - 7xy.4x{y^2}\\
= - 8{x^3}{y^2} + 3x{y^4} - 28{x^2}{y^3}\\
b)\left( {2{x^2} - \frac{1}{3}xy + {y^2}} \right).\left( { - 3{x^3}} \right)\\
= 2{x^2}.\left( { - 3{x^3}} \right) - \frac{1}{3}xy.\left( { - 3{x^3}} \right) + {y^2}.\left( { - 3{x^3}} \right)\\
= - 6{x^5} + {x^4}y - 3{x^3}{y^2}\\
c)\left( {2{x^2} - 3x - 1} \right).\left( {5x + 2} \right)\\
= \left( {2{x^2} - 3x - 1} \right).5x + \left( {2{x^2} - 3x - 1} \right).2\\
= 10{x^3} - 15{x^2} - 5x + 4{x^2} - 6x - 2\\
= 10{x^3} - 11{x^2} - 11x - 2
\end{array}\)
