Đáp án:
$\begin{array}{l}
1)\left( {1 - x} \right)\left( {2x + 1} \right) - {x^2}\left( {x - 2} \right) - {\left( {3 - x} \right)^2}\\
+ \left( {x + 1} \right)\left( {3 - 5x} \right) + {\left( {x + 2} \right)^3}\\
= 2x + 1 - 2{x^2} - x - {x^3} + 2{x^2} - \left( {9 - 6x + {x^2}} \right)\\
+ 3x - 5{x^2} + 3 - 5x + {x^3} + 6{x^2} + 12x + 8\\
= 17x + 3\\
2)\\
\left( {3x - 1} \right)\left( {x - 2} \right) + {\left( {x + 2} \right)^3} + \left( {4x + 1} \right){\left( {3 - x} \right)^2}\\
+ \left( {3 - x} \right)\left( {1 - x} \right)\left( {2x + 1} \right)\\
= 3{x^2} - 6x - x + 2 + {x^3} + 6{x^2} + 12x + 8\\
+ \left( {4x + 1} \right)\left( {{x^2} - 6x + 9} \right) + \left( {3 - 4x + {x^2}} \right)\left( {2x + 1} \right)\\
= {x^3} + 9{x^2} + 5x + 10\\
+ 4{x^3} - 24{x^2} + 36x + {x^2} - 6{x^2} + 9 + \\
+ 6x + 3 - 8{x^2} - 4x + 2{x^3} + {x^2}\\
= 7{x^3} - 27{x^2} + 43x + 19\\
3)\\
\left( {{x^2} + 1} \right)\left( {x + 1} \right) - {\left( {3 - x} \right)^2} - \left( {2 - x} \right)\left( {{x^2} + 1} \right)\\
+ \left( {1 - x} \right)\left( {2x + 1} \right)\\
= {x^3} + {x^2} + x + 1 - {x^2} + 6x - 9 - \\
\left( {2{x^2} + 2 - {x^3} - x} \right) + 2x + 1 - 2{x^2} - x\\
= - 4{x^2} + 9x - 9
\end{array}$
