Thực hiện phép tính:
a. \(\left( {5x - 2y} \right)\left( {{x^2} - xy + 1} \right)\)
\b. \(\left( {x - 1} \right)\left( {x + 1} \right)\left( {x + 2} \right)\)
c. \({1 \over 2}{x^2}{y^2}\left( {2x + y} \right)\left( {2x - y} \right)\)
a. \(\left( {5x - 2y} \right)\left( {{x^2} - xy + 1} \right)\) \( = 5{x^3} - 5{x^2}y + 5x - 2{x^2}y + 2x{y^2} - 2y\)
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\( = 5{x^3} - 7{x^2}y + 5x + 2x{y^2} - 2y\)
b. \(\left( {x - 1} \right)\left( {x + 1} \right)\left( {x + 2} \right)\) \( = \left( {{x^2} + x - x - 1} \right)\left( {x + 2} \right) = \left( {{x^2} - 1} \right)\left( {x + 2} \right)\)
\( = {x^3} + 2{x^2} - x - 2\)
c. \({1 \over 2}{x^2}{y^2}\left( {2x + y} \right)\left( {2x - y} \right)\) \( = {1 \over 2}{x^2}{y^2}\left( {4{x^2} - 2xy + 2xy - {y^2}} \right)\)
\( = {1 \over 2}{x^2}{y^2}\left( {4{x^2} - {y^2}} \right) = 2{x^4}{y^2} - {1 \over 2}{x^2}{y^4}\)