Đáp án + Giải thích các bước giải:
$(\dfrac{x}{y}+\dfrac{2y}{x})^{3}$
$=(\dfrac{x}{y})^{3}+3.(\dfrac{x}{y})^{2}.\dfrac{2y}{x}+3.\dfrac{x}{y}.(\dfrac{2y}{x})^{2}+(\dfrac{2y}{x})^{3}$
$=\dfrac{x^{3}}{y^{3}}+3.\dfrac{x^{2}}{y^{2}}.\dfrac{2y}{x}+3.\dfrac{x}{y}.\dfrac{(2y)^{2}}{x^{2}}+\dfrac{(2y)^{3}}{x^{3}}$
$=\dfrac{x^{3}}{y^{3}}+3.\dfrac{x^{2}}{y^{2}}.\dfrac{2y}{x}+3.\dfrac{x}{y}.\dfrac{4y^{2}}{x^{2}}+\dfrac{8y^{3}}{x^{3}}$
$=\dfrac{x^{3}}{y^{3}}+3.\dfrac{2x}{y}+3.\dfrac{4y}{x}+\dfrac{8y^{3}}{x^{3}}$
$=\dfrac{x^{3}}{y^{3}}+\dfrac{6x}{y}+\dfrac{12y}{x}+\dfrac{8y^{3}}{x^{3}}$
