Rút gọn các biểu thức sau
a. \(x\left( {2{x^2} - 3} \right) - {x^2}\left( {5x + 1} \right) + {x^2}\)
b. \(3x\left( {x - 2} \right) - 5x\left( {1 - x} \right) - 8\left( {{x^2} - 3} \right)\)
c. \({1 \over 2}{x^2}\left( {6x - 3} \right) - x\left( {{x^2} + {1 \over 2}} \right) + {1 \over 2}\left( {x + 4} \right)\)
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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. \({1 \over 2}{x^2}\left( {6x - 3} \right) - x\left( {{x^2} + {1 \over 2}} \right) + {1 \over 2}\left( {x + 4} \right)\)
\( = 3{x^3} - {3 \over 2}x - {x^3} - {1 \over 2}x + {1 \over 2}x + 2 = 2{x^3} - {3 \over 2}x + 2\)