Đề bài

Rút gọn các biểu thức:

a) \({\left( {x - 2} \right)^3} + {\left( {x + 2} \♉right)^🧸3} - 6x\left( {x + 2} \right)\left( {x - 2} \right)\).

b) \({\left( {2x - y}𒅌 \right)^3} + {\left( {2x + y} \right)^3}\).

Lời giải chi tiết

a) \({(x - 2)^3} + {(x + 2)^3} - 6x(x + 2🎶)(x - 2)\)

\( = \left( {{x^3} - 3.{x^2}.2 + 3.x{{.2}^2} - {2^3}} \right) + \𝔍left( {{x^3} + 3.{x^2}.2 + 3.x{{.2}^2} + {2^3}} \right) - 6x\left( {{x^2} - 4} \right)\)\( = {x^3} - 6{x^2} + 12x - 8 + {x^3} + 6{x^2} + 12x + 8 - 6{x^3} + 24x\)\( = \left( {{x^3} + {x^3} - 6{x^3}} \right) + \left( { - 6{x^2} + 6{x^2}} \right) + (12x + 12x + 24x) + ( - 8 + 8)\)

\( =  - 4{x^3} + 48x\)

b) \({(2x - y)^3} + {(2x + y)^3}\)

\( = \left[ {{{(2x)}^3} - 3.{{(2x)}^2}.y + 3.(2x).{y^2} - {y^3}} \right] + \left[ {{{(2x)}^3} + 3.{{(2x)}^2}.y + 3.(2x).{y^2} + {y^3}} \right]\)\( = 8{x^3} - 12{x^2}y + 6x{y^2} - {y^3} + 8{x^3} + 12{x^2}y + 6x{y^2} + {y^3}\)\( = \left( {8{x^3} + 8{x^3}} \right) + \left( { - 12{x^2}y + 12{x^2}y} \right) + \left( {6x{y^2} + 6x{y^2}} \right) + \left( { - {y^3} + {y^3}} \�🌊�right)\)

\( = 16{x^3} + 12x{y^2}\)