Phân tích đa thức thành nhân tử:

a) \(5{x^2}\left( {x - y} \right) - 15xy\left( {y - x} \right)\)

\( = 5{x^2}\left( {x - y} \right) + 15xy\left( {x - y} \right)\)

\[ = \left( {x - y} \right)\left( {5{x^2} + 15xy} \right)\]

\[ = 5x\left( {x - y} \right)\left( {x + 3y} \right).\]

b) \({\left( {x + y} \right)^2} - 6\left( {x + y} \right) + 9\)

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

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

c) \({x^2} - 5x + 6\)

\( = {x^2} - 2x - 3x + 6\)

\( = \left( {{x^2} - 2x} \right) - \left( {3x - 6} \right)\)

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

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