Question

Tính

\(\left(\dfrac{x}{y}-\dfrac{3y}{x}\right)^3\)

Answer 1

\(\left(\dfrac{x}{y}-\dfrac{3y}{x}\right)^3\\ =\left(\dfrac{x}{y}\right)^3-3.\left(\dfrac{x}{y}\right)^2.\left(\dfrac{3y}{x}\right)+3.\left(\dfrac{x}{y}\right).\left(\dfrac{3y}{x}\right)^2-\left(\dfrac{3y}{x}\right)^3\\ =\dfrac{x^3}{y^3}-3.\dfrac{x^2}{y^2}.\dfrac{3y}{x}+3.\dfrac{x}{y}.\dfrac{9y^2}{x^2}-\dfrac{27y^3}{x^3}\\ =\dfrac{x^3}{y^3}-\dfrac{9x}{y}+\dfrac{27y}{x}-\dfrac{27y^3}{x^3}\)

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Áp dụng HĐT số 5 : \(\left(A-B\right)^3=A^3-3A^2.B+3.A.B^2-B^3\)