Expand the expression \(( \dfrac{2}{x}-\dfrac{x}{2})^5\)

Asked by Pragya Singh | 1 year ago |  73

1 Answer

Solution :-

\(^5C_0 (\dfrac{2}{x})^5-^5C_1 (\dfrac{2}{x})^4\dfrac{x}{2}+\)

\( ^5C_2 (\dfrac{2}{x})^3(\dfrac{x}{2})^2-^5C_3 (\dfrac{2}{x})^2(\dfrac{x}{2})^3\)

\( +^5C_4 (\dfrac{2}{x})(\dfrac{x}{2})^4-^5C_5 \dfrac{x}{2}\)

\( \dfrac{32}{x^3}-5\dfrac{16}{x^4}(\dfrac{x}{2})+10(\dfrac{8}{x^3})(\dfrac{x^2}{4})-\)

\( 10(\dfrac{4}{x^2})(\dfrac{x^3}{8})+5(\dfrac{2}{x})(\dfrac{x^4}{16})-\dfrac{x^5}{32}\)

\( \dfrac{32}{x^5}-\dfrac{40}{x^3}+\dfrac{20}{x}-5x+\dfrac{5}{8}x^3-\dfrac{x^5}{32}\)

Answered by Abhisek | 1 year ago

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