Đề bài
Thực hiện các phép tính sau:
a) \((x - 1)(x + 2)\)
b) \((2 - x)(3x + 2)\)
c) \( - 4x(x - 2)(x + 2)\)
d) \((x + 3)({x^2} + 3x - 5)\)
e) \((x + 3)(x - 4)(x + 2)\)
f) \((2{x^3} - 3x - 1)(5x + 2)\)
Lời giải chi tiết
\(\eqalign{ & a)\,\,\left( {x - 1} \right)\left( {x + 2} \right) = {x^2} + 2x - x - 2 = {x^2} + x - 2 \cr & b)\,\,\left( {2 - x} \right)\left( {3x + 2} \right) = 6x + 4 - 3{x^2} - 2x = 4x + 4 - 3{x^2} \cr & c)\,\, - 4x\left( {x - 2} \right)\left( {x + 2} \right) = - 4x\left( {{x^2} + 2x - 2x - 4} \right) = - 4x\left( {{x^2} - 4} \right) = - 4{x^3} + 16x \cr & d)\,\,\left( {x + 3} \right)\left( {{x^2} + 3x - 5} \right) = {x^3} + 3{x^2} - 5x + 3{x^2} + 9x - 15 = {x^3} + 6{x^2} + 4x - 15 \cr & e)\,\,\left( {x + 3} \right)\left( {x - 4} \right)\left( {x + 2} \right) = \left( {x + 3} \right)\left( {{x^2} + 2x - 4x - 8} \right) \cr & = \left( {x + 3} \right)\left( {{x^2} - 2x - 8} \right) = {x^3} - 2{x^2} - 8x + 3{x^2} - 6x - 24 = {x^3} + {x^2} - 14x - 24 \cr & f)\,\,\left( {2{x^3} - 3x - 1} \right)\left( {5x + 2} \right) = 10{x^4} + 4{x^3} - 15{x^2} - 6x - 5x - 2 \cr & = 10{x^4} + 4{x^3} - 15{x^2} - 11x - 2 \cr} \)
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