Phân tích các đa thức sau thành nhân tử:

a)\[\,\left( {{x^2} + 2x + 1} \right) - 3\left( {x + 1} \right)\]

\[ = \,{\left( {x + 1} \right)^2} - 3\left( {x + 1} \right)\]

\[ = \,\left( {x + 1} \right)\left( {x + 1 - 3} \right)\]

\[ = \,\left( {x + 1} \right)\left( {x - 2} \right)\]

b) \[{x^2} - {y^2} + 4x + 4\]

\[ = \left( {{x^2} + 4x + 4} \right) - {y^2}\]

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

\[ = \left( {x + y + 2} \right)\left( {x - y + 2} \right)\]

c) \[{x^3} + 27 + \left( {x + 3} \right)\left( {x - 9} \right)\]

\[ = \left( {{x^3} + 27} \right) + \left( {x + 3} \right)\left( {x - 9} \right)\]

\[ = \,\left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) + \left( {x + 3} \right)\left( {x - 9} \right)\,\]

\[ = \left( {x + 3} \right)\left( {{x^2} - 3x + 9 + x - 9} \right)\,\]

\[ = \,\left( {x + 3} \right)\left( {{x^2} - 2x} \right)\]

\[ = \,x\left( {x + 3} \right)\left( {x - 2} \right)\]

d) \[2{x^3} - 4{x^2} - 2x + 4\]

\[ = \left( {2{x^3} - 4{x^2}} \right) - \left( {2x - 4} \right)\]

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

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

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