\(a)\) \(x\left( {2{x^2} - 3} \right) - {x^2}\left( {5x + 1} \right) + {x^2}\)
\( =2{x^3} - 3x - 5{x^3} - {x^2} + {x^2}\)
\(= - 3x - 3{x^3}\)
\(b)\) \(3x\left( {x - 2} \right) - 5x\left( {1 - x} \right) - 8\left( {{x^2} - 3} \right)\)
\( = 3{x^2} - 6x - 5x + 5{x^2} - 8{x^2} + 24 \)
\(= - 11x + 24\)
\(c)\dfrac{1 }{ 2}{x^2}\left( {6x - 3} \right) - x\left( {{x^2} + \dfrac{1 }{ 2}} \right) \\+ \dfrac{1 }{ 2}\left( {x + 4} \right)\)
\( = 3{x^3} - \dfrac{3 }{ 2}x^2 - {x^3} - \dfrac{1 }{ 2}x + \dfrac{1 }{ 2}x + 2\)
\(= 2{x^3} - \dfrac{3 }{ 2}x^2 + 2\)
