Phân tích đa thức thành nhân tử:

a) \(2x\left( {x + 2} \right) + {x^2}\left( { - x - 2} \right)\)

\( = 2x\left( {x + 2} \right) - {x^2}\left( {x + 2} \right)\)

\( = \left( {x + 2} \right)\left( {2x - {x^2}} \right)\)

\( = x\left( {x + 2} \right)\left( {2 - x} \right)\).

b) \({x^6} - 1\)

\( = {\left( {{x^3}} \right)^2} - {1^2}\)

\( = \left( {{x^3} - 1} \right)\left( {{x^3} + 1} \right)\)

\( = \left( {x - 1} \right)\left( {{x^2} + x + 1} \right)\left( {x + 1} \right)\left( {{x^2} - x + 1} \right).\)

) \(2{x^2} - 3x + 1\)

\( = 2{x^2} - 2x - x + 1\)

\( = \left( {2{x^2} - 2x} \right) - \left( {x - 1} \right)\)

\( = 2x\left( {x - 1} \right) - \left( {x - 1} \right)\)

\( = \left( {x - 1} \right)\left( {2x - 1} \right).\)