Đề bài

Tính: a) \(x + 2y + \left( {x - y} \right)\) b) \(2x - y - \left( {3x - 5y} \right)\) c) \(3{x^2} - 4{y^2} + 6xy + 7 + \left( { - {x^2} + {y^2} - 8xy + 9x + 1} \right)\) d) \(4{x^2}y - 2x{y^2} + 8 - \left( {3{x^2}y + 9x{y^2} - 12xy + 6} \right)\)

Lời giải chi tiết

a)\(x + 2y + \left( {x - y} \right)\)\( = x + 2y + x - y\)\( = \left( {x + x} \right) + \left( {2y - y} \right)\)\( = 2x + y\)b)\(2x - y - \left( {3x - 5y} \right)\)\( = 2x - y - 3x + 5y\)\( = \left( {2x - 3x} \right) + \left( { - y + 5y} \right)\)\( =  - x + 4y\)c)\(3{x^2} - 4{y^2} + 6xy + 7 + \left( { - {x^2} + {y^2} - 8xy + 9x + 1} \right)\)\( = 3{x^2} - 4{y^2} + 6xy + 7 - {x^2} + {y^2} - 8xy + 9x + 1\)\( = \left( {3{x^2} - {x^2}} \right) + \left( { - 4{y^2} + {y^2}} \right) + \left( {6xy - 8xy} \right) + 9x + \left( {7 + 1} \right)\)\( = 2{x^2} - 3{y^2} - 2xy + 9x + 8\)d)\(4{x^2}y - 2x{y^2} + 8 - \left( {3{x^2}y + 9x{y^2} - 12xy + 6} \right)\)\( = 4{x^2}y - 2x{y^2} + 8 - 3{x^2}y - 9x{y^2} + 12xy - 6\)\( = \left( {4{x^2}y - 3{x^2}y} \right) + \left( { - 2x{y^2} - 9x{y^2}} \right) + 12xy + \left( {8 - 6} \right)\)\( = {x^2}y - 11x{y^2} + 12xy + 2\)