\[\begin{array}{l}
a){\rm{ }}2x\left( {x{\rm{ }} - {\rm{ }}3y} \right){\rm{ }} + {\rm{ }}3y\left( {2x{\rm{ }} - {\rm{ }}5y} \right){\rm{ }}\\
{\rm{ = 2}}{{\rm{x}}^2} - 6xy + 6xy - 15{y^2}\\
= 2{x^2} - 15{y^2}\\
c){\rm{ }}\left( {6x{\rm{ }} - {\rm{ }}1} \right)\left( {3{\rm{ }} + {\rm{ }}x} \right){\rm{ }} + {\rm{ }}\left( {2x{\rm{ }} + {\rm{ }}5} \right)\left( { - {\rm{ }}3x} \right)\\
{\rm{ = 18x + 6}}{{\rm{x}}^2}{\rm{ - 3 - x - 6}}{{\rm{x}}^2}{\rm{ - 15x}}\\
{\rm{ = 2x - 3 }}\\
e){\rm{ }}\left( {x{\rm{ }} - {\rm{ }}3} \right)\left( {2x{\rm{ }} - {\rm{ }}1} \right){\rm{ }} - {\rm{ }}\left( {x{\rm{ }} - {\rm{ }}7} \right)\left( {2x{\rm{ }} - {\rm{ }}1} \right)\\
{\rm{ = 2}}{{\rm{x}}^2}{\rm{ - x - 6x + 3 - }}\left( {2{x^2} - x - 14x + 7} \right)\\
{\rm{ = 2}}{{\rm{x}}^2}{\rm{ - 7x + 3 - 2}}{{\rm{x}}^2}{\rm{ + 15x - 7}}\\
{\rm{ = 8x - 4 }}\\
b){\rm{ }}\left( {2x{\rm{ }} - {\rm{ }}3} \right)\left( {x{\rm{ }} + {\rm{ }}2} \right){\rm{ }} - {\rm{ }}\left( {4x{\rm{ }} - {\rm{ }}2} \right)\left( {x{\rm{ }} - {\rm{ }}5} \right)\\
{\rm{ = 2}}{{\rm{x}}^2}{\rm{ + 4x - 3x - 6 - }}\left( {4{x^2} - 20x - 2x + 10} \right)\\
{\rm{ = 2}}{{\rm{x}}^2}{\rm{ + x - 6 - 4}}{{\rm{x}}^2}{\rm{ + 22x - 10}}\\
{\rm{ = - 2}}{{\rm{x}}^2}{\rm{ + 23x - 16 }}\\
d){\rm{ }}5x\left( {x{\rm{ }} - {\rm{ }}1} \right){\rm{ }} - {\rm{ }}\left( {x{\rm{ }} + {\rm{ }}2} \right)\left( {5x{\rm{ }} - {\rm{ }}7} \right)\\
{\rm{ = 5}}{{\rm{x}}^2}{\rm{ - 5x - }}\left( {5{x^2} - 7x + 10x - 14} \right)\\
{\rm{ = 5}}{{\rm{x}}^2}{\rm{ - 5x - 5}}{{\rm{x}}^2}{\rm{ - 3x + 14}}\\
{\rm{ = - 8x + 14 }}\\
f){\rm{ }}3x\left( {2x{\rm{ }} - {\rm{ }}8} \right){\rm{ }} + {\rm{ }}\left( {6x{\rm{ }} - {\rm{ }}2} \right)\left( {5{\rm{ }} - {\rm{ }}x} \right){\rm{ }}\\
{\rm{ = 6}}{{\rm{x}}^2} - 24x + 30x - 6{x^2} - 10 + 2x\\
= 8x - 10
\end{array}\]