Thực hiện phép tính:

a) \(7{x^2}{y^5} - \frac{7}{3}{y^2}\left( {3{x^2}{y^3} + 1} \right)\);

b) \(\frac{1}{2}x\left( {{x^2} + {y^2}} \right) - \frac{3}{2}{y^2}\left( {x + 1} \right) - \frac{1}{{\sqrt 4 }}{x^3}\);

c) (x + y)(x2 + y2 + 3xy) ‒ x3 ‒ y3;

d) (‒132xn + 1y10zn + 2 + 143xn + 2y12zn) : (11xny9zn) với n là số tự nhiên.

Lời giải

a) \(7{x^2}{y^5} - \frac{7}{3}{y^2}\left( {3{x^2}{y^3} + 1} \right)\)

\( = 7{x^2}{y^5} - 7{x^2}{y^5} - \frac{7}{3}{y^2}\)

\( = - \frac{7}{3}{y^2}\).

b) \(\frac{1}{2}x\left( {{x^2} + {y^2}} \right) - \frac{3}{2}{y^2}\left( {x + 1} \right) - \frac{1}{{\sqrt 4 }}{x^3}\)

\( = \frac{1}{2}{x^3} + \frac{1}{2}x{y^2} - \frac{3}{2}x{y^2} - \frac{3}{2}{y^2} - \frac{1}{2}{x^3}\)

\( = \left( {\frac{1}{2}{x^3} - \frac{1}{2}x} \right) + \left( {\frac{1}{2}x{y^2} - \frac{3}{2}x{y^2}} \right) - \frac{3}{2}{y^2}^3\)

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

c) (x + y)(x2 + y2 + 3xy) ‒ x3 ‒ y3

= (x + y)(x2 + y2 + 3xy) ‒ (x3 + y3)

= (x + y)(x2 + y2 + 3xy) ‒ (x + y)(x2 ‒ xy + y2)

= (x + y)( x2 + y2 + 3xy ‒ x2 + xy ‒ y2)

= (x + y).4xy

= 4x2y + 4xy2.

d) (‒132xn + 1y10zn + 2 + 143xn + 2y12zn) : (11xny9zn)

= (‒132xn + 1y10zn + 2 : 11xny9zn) + (143xn + 2y12zn : 11xny9zn)

= (‒132 : 11)(xn + 1 : xn)(y10 : y9)(zn + 2 : zn) + (143 : 11)(xn + 2 : xn)(y12 : y9)(zn : zn)

= ‒12xyz2 + 13x2y3.