Bài 1. Ta có:
\(\left( {{x^2} - x + 5} \right)\left( {{x^2} + 1} \right) \)
\(= {x^4} + {x^2} - {x^3} - x + 5{x^2} + 5.\)
\(={x^4} - {x^3} + 6{x^2} - x + 5\) .
Vậy \(m = 5.\)
Bài 2.
\(\left( {2x - 1} \right)\left( {3x + 2} \right)\left( {3 - x} \right) \)
\(= \left( {2x - 1} \right)\left[ {\left( {3x + 2} \right)\left( {3 - x} \right)} \right]\)
\(=\left( {2x - 1} \right)\left( {9x - 3{x^2} + 6 - 2x} \right) \)
\(= \left( {2x - 1} \right)\left( {7x - 3{x^2} + 6} \right)\)
\(=14{x^2} - 6{x^3} + 12x - 7x + 3{x^2} - 6\)
\(= - 6{x^3} + 17{x^2} + 5x - 6.\)
Bài 3. Ta có:
\(\left( {x - y} \right)\left( {{x^4} + {x^3}y + {x^2}{y^2} + x{y^3} + {y^4}} \right)\)
\(={x^5} + {x^4}y + {x^3}{y^2} + {x^2}{y^3} + x{y^4} - {x^4}y - {x^3}{y^2} - {x^2}{y^3} - x{y^4} - {y^5}\)
\(={x^5} - {y^5}\) (đpcm)
