Question

Rút gọn biểu thức: \(\left( {3{x^2} - 5xy - 4{y^2}} \right).\left( {2{x^2} + {y^2}} \right) + \left( {2{x^4}y - {x^3}{y^3} - {x^2}{y^4}} \right):\left( {\dfrac{1}{5}xy} \right)\) 

Answer 1

\(\left( {3{x^2} - 5xy - 4{y^2}} \right).\left( {2{x^2} + {y^2}} \right) + \left( {2{x^4}y^2 + {x^3}{y^3} + {x^2}{y^4}} \right):\left( {\dfrac{1}{5}xy} \right)\\\)

\(= 3{x^2}.2{x^2} + 3{x^2}.{y^2} - 5xy.2{x^2} - 5xy.{y^2} - 4{y^2}.2{x^2} - 4{y^2}.{y^2} + 2{x^4}y^2:\left( {\dfrac{1}{5}xy} \right) + {x^3}{y^3}:\left( {\dfrac{1}{5}xy} \right) + {x^2}{y^4}:\left( {\dfrac{1}{5}xy} \right)\\\)

\(= 6{x^4} + 3{x^2}{y^2} - 10{x^3}y - 5x{y^3} - 8{x^2}{y^2} - 4{y^4} + 10{x^3}y + 5{x^2}{y^2} + 5x{y^3}\\\)

\(= 6{x^4} - 4{y^4}+ ( - 10{x^3}y + 10{x^3}y) + \left( { - 5x{y^3} + 5x{y^3}} \right) + \left( {3{x^2}{y^2} - 8{x^2}{y^2} + 5{x^2}{y^2}} \right)\\\)

\(= 6{x^4} - 4{y^4}\)