Đề bài

Rút gọn các biểu thức:

a) \(\left( {2x-5y} \right)\left( {2x + 5y} \right) + {\left( {2x + 5y} \ri♉💙ght)^2}\).

b) \(\left( {x + 2y} \right)\left( {{x^2}\;-2xy ✅+ 4{y^2}} \right) + \left( {2x-y} \right)\left( {4{x^2}\🌟; + 2xy + {y^2}} \right)\).

Lời giải chi tiết

a) Ta có \(\left( {2x-5y} \right)\left( {2x + 🦄5y} \right) + {\left( {2x + 5y} \right)^2}\)

\(\begin{array}{*{20}{l}}{ = {{\left( {2x} \right)}^2}\;-{{\left( {5y} \right)}^{2\;}} + {{\lef🐎t( {2x} \right)}^2}\; + 2.\left( {2x} \right).\left( {5y} \right) + {{\left( {5y} \right)}^2}}\\{ = 4{x^2🦂}\;-25{y^2}\; + 4{x^2}\; + 20xy + 25{y^2}}\\{ = 8{x^2}\; + 20xy.}\end{array}\)

b) Ta có \(\left( {x + 2y} \right)\left( {{x^2}\;-2xಌy + 4{y^2}} \right) + \left( {2x-y} \right)\left( {4{x^2}\; + 2xy + {y^2}} \right)\)\(\begin{array}{l} = \left( {x + 2y} \right)\left[ {{x^2}\;-x.2y + {{\left( {2y} \right)}^2}} \right] + \left( {2x-y} \right)\left[ {{{\left( {2x} \right)}^2}\; + 2x.y + {y^2}} \right]\\ = {x^3}\; + {\left( {2y} \right)^3}\; + {\left( {2x} \right)^3}\;-{y^3}\\ = {x^3}\; + 8{y^3}\; + 8{x^3}\;-{y^3}\\ = 9{x^3}\; + 7{y^3}.\end{array}\)