Đáp án:
\(\begin{array}{l}
1) - 2{x^3} - 13{x^2} - x - 12\\
2) - 5{x^3} - 38{x^2} - 76x - 46\\
3){x^3} - 20{x^2} + 58x + 69\\
4) - 18{x^3} - 46{x^2} - 8x + 16\\
5) - 22{x^3} + 9{x^2} + 29x + 19
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
1) - 3x\left( {{x^2} + 4x + 4} \right) + \left( {x + 3} \right)\left( {{x^2} - 1} \right) - 4{x^2} + 12x - 9\\
= - 3{x^3} - 12{x^2} - 12x + {x^3} - x + 3{x^2} - 3 - 4{x^2} + 12x - 9\\
= - 2{x^3} - 13{x^2} - x - 12\\
2)\left( {{x^2} - 9} \right)\left( {x + 2} \right) - {x^3} + 3x + {x^2} - 3 - 5x\left( {{x^2} + 8x + 16} \right) - {x^2} + 10x - 25\\
= {x^3} + 2{x^2} - 9x - 18 - {x^3} + 13x - 28 - 5{x^3} - 40{x^2} - 80x\\
= - 5{x^3} - 38{x^2} - 76x - 46\\
3)2x\left( {{x^2} - 8x + 16} \right) - \left( {x + 5} \right)\left( {{x^2} - 4} \right) + 2\left( {{x^2} + 10x + 25} \right) - {x^2} + 2x - 1\\
= 2{x^3} - 16{x^2} + 32x - {x^3} + 4x - 5{x^2} + 20 + 2{x^2} + 20x + 50 - {x^2} + 2x - 1\\
= {x^3} - 20{x^2} + 58x + 69\\
4){x^2} + 10x + 25 - 4x\left( {4{x^2} + 12x + 9} \right) - \left( {2x - 1} \right)\left( {{x^2} - 9} \right)\\
= {x^2} + 10x + 25 - 16{x^3} - 48{x^2} - 36x - 2{x^3} + 18x + {x^2} - 9\\
= - 18{x^3} - 46{x^2} - 8x + 16\\
5) - 2x\left( {9{x^2} - 4} \right) + 5\left( {{x^2} + 4x + 4} \right) - \left( {x - 1} \right)\left( {4{x^2} - 1} \right)\\
= - 18{x^3} + 8x + 5{x^2} + 20x + 20 - 4{x^3} + x + 4{x^2} - 1\\
= - 22{x^3} + 9{x^2} + 29x + 19
\end{array}\)
