Câu 1

Đề bài

Thực hiện phép tính:

\(a){\left( {2{\rm{x}} + y} \right)^2} + {\left( {5{\rm{x}} - y} \right)^2} + 2\left( {2{\rm{x}} + y} \right)\left( {5{\rm{x}} - y} \right)\)

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

Lời giải chi tiết

\(\begin{array}{l}a){\left( {2{\rm{x}} + y} \right)^2} + {\left( {5{\rm{x}} - y} \right)^2} + 2\left( {2{\rm{x}} + y} \right)\left( {5{\rm{x}} - y} \right)\\ = 4{{\rm{x}}^2} + 4{\rm{x}}y + {y^2} + 25{{\rm{x}}^2} - 10{\rm{x}}y + {y^2} + 2.\left( {10{{\rm{x}}^2} - 2{\rm{x}}y + 5{\rm{x}}y - {y^2}} \right)\\ = 4{{\rm{x}}^2} + 4{\rm{x}}y + {y^2} + 25{{\rm{x}}^2} - 10{\rm{x}}y + {y^2} + 20{{\rm{x}}^2} - 4{\rm{x}}y + 10xy - 2{y^2}\\ = 49{{\rm{x}}^2}\end{array}\)

\(\begin{array}{l}b)\left( {2{\rm{x}} - {y^3}} \right)\left( {2{\rm{x}} + {y^3}} \right) - \left( {2{\rm{x}} - {y^2}} \right)\left( {4{{\rm{x}}^2} + 2{\rm{x}}{y^2} + {y^4}} \right)\\ = 4{{\rm{x}}^2} - {y^6} - 8{{\rm{x}}^3} - 4{{\rm{x}}^2}{y^2} - 2{\rm{x}}{y^4} + 4{{\rm{x}}^2}{y^2} + 2{\rm{x}}{y^4} + {y^6}\\ =  - 8{{\rm{x}}^3} + 4{{\rm{x}}^2}\end{array}\)