Phân tích các đa thức sau thành nhân tử:

a) \({\left( {x + 1} \right)^2} + 1 + x\)

\( = \left( {x + 1} \right)\left( {x + 1} \right) + \left( {x + 1} \right)\)

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

b) \[{\left( {x + y} \right)^3} - {\left( {x - y} \right)^3}\]

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

\[ = 6{x^2}y + 2{y^3} = 2y\left( {3{x^2} + {y^2}} \right)\].

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

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

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

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

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

d) \[49{y^2} - {x^2} + 6x - 9\]

\[ = 49{y^2} - \left( {{x^2} - 6x + 9} \right)\]

\[ = {\left( {7y} \right)^2} - {\left( {x - 3} \right)^2}\]

\[ = \left( {7y - x + 3} \right)\left( {7y + x - 3} \right)\]