Phân tích đa thức thành nhân tử:

a) \(5\left( {y - 3} \right) - x\left( {3 - y} \right)\)

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

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

b) \({x^6} + {y^9}\)

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

\( = \left( {{x^2} + {y^3}} \right)\left( {{x^4} - {x^2}{y^3} + {y^6}} \right)\).

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

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

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

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

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