Đề bài
Thực hiện các phép tính:
a] \[2x[x - 5] + [x - 2][x + 3]\] ;
b] \[[2x - 5][1 - x] - [x - 3][ - 2x]\] ;
c] \[[4x - 3][4x - 3] - [3x + 2][3x - 2]\] ;
d] \[[x - 2][x - 1][x + 3] - {x^2}[x - 5]\] .
Lời giải chi tiết
\[\eqalign{ & a]\,\,2x\left[ {x - 5} \right] + \left[ {x - 2} \right]\left[ {x + 3} \right] \cr & = 2{x^2} - 10x + {x^2} + 3x - 2x - 6 \cr & = 3{x^2} - 9x - 6 \cr & b]\,\,\left[ {2x - 5} \right]\left[ {1 - x} \right] - \left[ {x - 3} \right]\left[ { - 2x} \right] \cr & = \left[ {2x - 2{x^2} - 5 + 5x} \right] - \left[ { - 2{x^2} + 6x} \right] \cr & = 2x - 2{x^2} - 5 + 5x + 2{x^2} - 6x \cr & = x - 5 \cr & c]\,\,\left[ {4x - 3} \right]\left[ {4x - 3} \right] - \left[ {3x + 2} \right]\left[ {3x - 2} \right] \cr & = 16{x^2} - 24x + 9 - \left[ {9{x^2} - 4} \right] \cr & = 16{x^2} - 24x + 9 - 9{x^2} + 4 \cr & = 7{x^2} - 24x + 13 \cr & d]\,\,\left[ {x - 2} \right]\left[ {x - 1} \right]\left[ {x + 3} \right] - {x^2}\left[ {x - 5} \right] \cr & = \left[ {x - 2} \right]\left[ {{x^2} + 3x - x - 3} \right] - {x^2}\left[ {x - 5} \right] \cr & = \left[ {x - 2} \right]\left[ {{x^2} + 2x - 3} \right] - {x^2}\left[ {x - 5} \right] \cr & = {x^3} + 2{x^2} - 3x - 2{x^2} - 4x + 6 - {x^3} + 5{x^2} \cr & = 5{x^2} - 7x + 6 \cr} \]