Rút gọn các biểu thức sau:

a) \[\left( {x + y} \right) + \left( {3x - y} \right)\];

b) \[\left( { - 3xy} \right) \cdot 2xy + \left( {18{x^4}{y^3} - 9{x^5}{y^3}} \right):\left( {3{x^2}y} \right)\];

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

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

\[ = x + y + 3x - y\]

\[ = \left( {x + 3x} \right) + \left( {y - y} \right) = 4x\].

b) \[\left( { - 3xy} \right) \cdot 2xy + \left( {18{x^4}{y^3} - 9{x^5}{y^3}} \right):\left( {3{x^2}y} \right)\]

\[ = \left( { - 3xy} \right) \cdot 2xy + 18{x^4}{y^3}:\left( {3{x^2}y} \right) - 9{x^5}{y^3}:\left( {3{x^2}y} \right)\]

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

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

\[ = {y^2} - 4{x^2} + 4{x^2} + 4xy + {y^2}\]

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