Rút gọn biểu thức: (a) x(x^2+2xy+3x)−3x^2+2x^2y. (b) 3x^2+(x+y)(x−y).

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

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

\( = {x^3} + 4{x^2}y\)

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

\( = 3{x^2} + {x^2} - {y^2} = 4{x^2} - {y^2}\)

c) \(\left( {10{x^5}{y^3} - 15{x^5}{y^2}} \right):5{x^4}{y^2} - \left( {2x - 3} \right)\left( {x + y} \right)\)

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

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

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