Đáp án:

\(\begin{array}{l}
1,\\
 - 2{x^3} - 13{x^2} - x - 12\\
2,\\
 - 5{x^3} - 38{x^2} - 76x - 46\\
3,\\
{x^3} - 12{x^2} + 58x + 69\\
4,\\
 - 18{x^3} - 48{x^2} - 8x + 16\\
5,\\
 - 22{x^3} + 9{x^2} + 29x + 19\\
6,\\
41{x^3} - 11{x^2} - 200x - 154\\
7,\\
 - 5{x^4} - {x^3} + 5{x^2} + 16x - 9
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
1,\\
 - 3x.{\left( {x + 2} \right)^2} + \left( {x + 3} \right).\left( {x - 1} \right)\left( {x + 1} \right) - {\left( {2x - 3} \right)^2}\\
 =  - 3x.\left( {{x^2} + 2.x.2 + {2^2}} \right) + \left( {x + 3} \right).\left( {{x^2} - {1^2}} \right) - \left[ {{{\left( {2x} \right)}^2} - 2.2x.3 + {3^2}} \right]\\
 =  - 3x.\left( {{x^2} + 4x + 4} \right) + \left( {x + 3} \right).\left( {{x^2} - 1} \right) - \left( {4{x^2} - 12x + 9} \right)\\
 = \left( { - 3{x^3} - 12{x^2} - 12x} \right) + \left( {{x^3} - x + 3{x^2} - 3} \right) - \left( {4{x^2} - 12x + 9} \right)\\
 =  - 3{x^3} - 12{x^2} - 12x + {x^3} + 3{x^2} - x - 3 - 4{x^2} + 12x - 9\\
 = \left( { - 3{x^3} + {x^3}} \right) + \left( { - 12{x^2} + 3{x^2} - 4{x^2}} \right) + \left( { - 12x - x + 12x} \right) + \left( { - 3 - 9} \right)\\
 =  - 2{x^3} - 13{x^2} - x - 12\\
2,\\
\left( {x - 3} \right)\left( {x + 3} \right)\left( {x + 2} \right) - \left( {x - 1} \right)\left( {{x^2} - 3} \right) - 5x.{\left( {x + 4} \right)^2} - {\left( {x - 5} \right)^2}\\
 = \left( {{x^2} - {3^2}} \right)\left( {x + 2} \right) - \left( {{x^3} - 3x - {x^2} + 3} \right) - 5x.\left( {{x^2} + 2.x.4 + {4^2}} \right) - \left( {{x^2} - 2.x.5 + {5^2}} \right)\\
 = \left( {{x^2} - 9} \right).\left( {x + 2} \right) - \left( {{x^3} - {x^2} - 3x + 3} \right) - 5x.\left( {{x^2} + 8x + 16} \right) - \left( {{x^2} - 10x + 25} \right)\\
 = \left( {{x^3} + 2{x^2} - 9x - 18} \right) - \left( {{x^3} - {x^2} - 3x + 3} \right) - \left( {5{x^3} + 40{x^2} + 80x} \right) - \left( {{x^2} - 10x + 25} \right)\\
 = {x^3} + 2{x^2} - 9x - 18 - {x^3} + {x^2} + 3x - 3 - 5{x^3} - 40{x^2} - 80x - {x^2} + 10x - 25\\
 = \left( {{x^3} - {x^3} - 5{x^3}} \right) + \left( {2{x^2} + {x^2} - 40{x^2} - {x^2}} \right) + \left( { - 9x + 3x - 80x + 10x} \right) + \left( { - 18 - 3 - 25} \right)\\
 =  - 5{x^3} - 38{x^2} - 76x - 46\\
3,\\
2x.{\left( {x - 4} \right)^2} - \left( {x + 5} \right)\left( {x - 2} \right)\left( {x + 2} \right) + 2.{\left( {x + 5} \right)^2} - {\left( {x - 1} \right)^2}\\
 = 2x.\left( {{x^2} - 2.x.4 + {4^2}} \right) - \left( {x + 5} \right).\left( {{x^2} - {2^2}} \right) + 2.\left( {{x^2} + 2.x.5 + {5^2}} \right) - \left( {{x^2} - 2.x.1 + {1^2}} \right)\\
 = 2x.\left( {{x^2} - 8x + 16} \right) - \left( {x + 5} \right).\left( {{x^2} - 4} \right) + 2.\left( {{x^2} + 10x + 25} \right) - \left( {{x^2} - 2x + 1} \right)\\
 = \left( {2{x^3} - 16{x^2} + 32x} \right) - \left( {{x^3} - 4x + 5{x^2} - 20} \right) + \left( {2{x^2} + 20x + 50} \right) - \left( {{x^2} - 2x + 1} \right)\\
 = 2{x^3} - 16{x^2} + 32x - {x^3} + 4x - 5{x^2} + 20 + 2{x^2} + 20x + 50 - {x^2} + 2x - 1\\
 = \left( {2{x^3} - {x^3}} \right) + \left( { - 16{x^2} - 5{x^2} + 10{x^2} - {x^2}} \right) + \left( {32x + 4x + 20x + 2x} \right) + \left( {20 + 50 - 1} \right)\\
 = {x^3} - 12{x^2} + 58x + 69\\
4,\\
{\left( {x + 5} \right)^2} - 4x.{\left( {2x + 3} \right)^2} - \left( {2x - 1} \right)\left( {x + 3} \right)\left( {x - 3} \right)\\
 = \left( {{x^2} + 2.x.5 + {5^2}} \right) - 4x.\left[ {{{\left( {2x} \right)}^2} + 2.2x.3 + {3^2}} \right] - \left( {2x - 1} \right)\left( {{x^2} - {3^2}} \right)\\
 = \left( {{x^2} + 10x + 25} \right) - 4x.\left( {4{x^2} + 12x + 9} \right) - \left( {2x - 1} \right)\left( {{x^2} - 9} \right)\\
 = \left( {{x^2} + 10x + 25} \right) - \left( {16{x^3} + 48{x^2} + 36x} \right) - \left( {2{x^3} - 18x - {x^2} + 9} \right)\\
 = {x^2} + 10x + 25 - 16{x^3} - 48{x^2} - 36x - 2{x^3} + 18x + {x^2} - 9\\
 = \left( { - 16{x^3} - 2{x^3}} \right) + \left( {{x^2} - 48{x^2} + {x^2}} \right) + \left( {10x - 36x + 18x} \right) + \left( {25 - 9} \right)\\
 =  - 18{x^3} - 48{x^2} - 8x + 16\\
5,\\
 - 2x.\left( {3x + 2} \right)\left( {3x - 2} \right) + 5.{\left( {x + 2} \right)^2} - \left( {x - 1} \right)\left( {2x - 1} \right)\left( {2x + 1} \right)\\
 =  - 2x.\left[ {{{\left( {3x} \right)}^2} - {2^2}} \right] + 5.\left( {{x^2} + 2.x.2 + {2^2}} \right) - \left( {x - 1} \right).\left[ {{{\left( {2x} \right)}^2} - {1^2}} \right]\\
 =  - 2x.\left( {9{x^2} - 4} \right) + 5.\left( {{x^2} + 4x + 4} \right) - \left( {x - 1} \right)\left( {4{x^2} - 1} \right)\\
 =  - \left( {18{x^3} - 8x} \right) + \left( {5{x^2} + 20x + 20} \right) - \left( {4{x^3} - x - 4{x^2} + 1} \right)\\
 =  - 18{x^3} + 8x + 5{x^2} + 20x + 20 - 4{x^3} + x + 4{x^2} - 1\\
 = \left( { - 18{x^3} - 4{x^3}} \right) + \left( {5{x^2} + 4{x^2}} \right) + \left( {8x + 20x + x} \right) + \left( {20 - 1} \right)\\
 =  - 22{x^3} + 9{x^2} + 29x + 19\\
6,\\
\left( {7x - 8} \right)\left( {7x + 8} \right) - 10{\left( {2x + 3} \right)^2} + 5x.{\left( {3x - 2} \right)^2} - 4x.{\left( {x - 5} \right)^2}\\
 = \left[ {{{\left( {7x} \right)}^2} - {8^2}} \right] - 10.\left[ {{{\left( {2x} \right)}^2} + 2.2x.3 + {3^2}} \right] + 5x.\left[ {{{\left( {3x} \right)}^2} - 2.3x.2 + {2^2}} \right] - 4x.\left( {{x^2} - 2.x.5 + {5^2}} \right)\\
 = \left( {49{x^2} - 64} \right) - 10.\left( {4{x^2} + 12x + 9} \right) + 5x.\left( {9{x^2} - 12x + 4} \right) - 4x.\left( {{x^2} - 10x + 25} \right)\\
 = 49{x^2} - 64 - \left( {40{x^2} + 120x + 90} \right) + \left( {45{x^3} - 60{x^2} + 20x} \right) - \left( {4{x^3} - 40{x^2} + 100x} \right)\\
 = 49{x^2} - 64 - 40{x^2} - 120x - 90 + 45{x^3} - 60{x^2} + 20x - 4{x^3} + 40{x^2} - 100x\\
 = \left( {45{x^3} - 4{x^3}} \right) + \left( {49{x^2} - 40{x^2} - 60{x^2} + 40{x^2}} \right) + \left( { - 120x + 20x - 100x} \right) + \left( { - 64 - 90} \right)\\
 = 41{x^3} - 11{x^2} - 200x - 154\\
7,\\
\left( {{x^2} - 3} \right)\left( {{x^2} + 3} \right) - 5{x^2}{\left( {x + 1} \right)^2} - \left( {{x^2} - 3x} \right)\left( {{x^2} - 2x} \right) + 4x.{\left( {x + 2} \right)^2}\\
 = \left[ {{{\left( {{x^2}} \right)}^2} - {3^2}} \right] - 5{x^2}.\left( {{x^2} + 2.x.1 + {1^2}} \right) - \left( {{x^4} - 2{x^3} - 3{x^3} + 6{x^2}} \right) + 4x.\left( {{x^2} + 2.x.2 + {2^2}} \right)\\
 = \left( {{x^4} - 9} \right) - 5{x^2}.\left( {{x^2} + 2x + 1} \right) - \left( {{x^4} - 5{x^3} + 6{x^2}} \right) + 4x.\left( {{x^2} + 4x + 4} \right)\\
 = {x^4} - 9 - \left( {5{x^4} + 10{x^3} + 5{x^2}} \right) - \left( {{x^4} - 5{x^3} + 6{x^2}} \right) + \left( {4{x^3} + 16{x^2} + 16x} \right)\\
 = {x^4} - 9 - 5{x^4} - 10{x^3} - 5{x^2} - {x^4} + 5{x^3} - 6{x^2} + 4{x^3} + 16{x^2} + 16x\\
 = \left( {{x^4} - 5{x^4} - {x^4}} \right) + \left( { - 10{x^3} + 5{x^3} + 4{x^3}} \right) + \left( { - 5{x^2} - 6{x^2} + 16{x^2}} \right) + 16x - 9\\
 =  - 5{x^4} - {x^3} + 5{x^2} + 16x - 9
\end{array}\)