Phân tích đa thức thành nhân tử:

a) \(3{x^3} - 6x;\)                                   b) \({x^2}\left( {x - 1} \right) + 25\left( {1 - x} \right);\)

c) \(5{x^2} - 10xy + 5{y^2} - 20{z^2};\)        d) \({x^3} - 3{x^2} + 3x - 1.\)

a) \(3{x^3} - 6x\)

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

c) \(5{x^2} - 10xy + 5{y^2} - 20{z^2}\)

\( = 5\left( {{x^2} - 2xy + {y^2} - 4{z^2}} \right)\)

\( = 5\left[ {{{\left( {x - y} \right)}^2} - {{\left( {2z} \right)}^2}} \right]\)

\( = 5\left( {x - y - 2z} \right)\left( {x - y + 2z} \right).\)

b) \({x^2}\left( {x - 1} \right) + 25\left( {1 - x} \right)\)

\( = {x^2}\left( {x - 1} \right) - 25\left( {x - 1} \right)\)

\( = \left( {x - 1} \right)\left( {{x^2} - 25} \right)\)

\( = \left( {x - 1} \right)\left( {x - 5} \right)\left( {x + 5} \right).\)

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

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