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

Asked by Pragya Singh | 1 year ago |  73

##### 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

### Related Questions

#### Find the term independent of x in the expansion of (3/2 x2 – 1/3x)9

Find the term independent of x in the expansion of $$(\dfrac{3}{2x^2} – \dfrac{1}{3x})^9$$

#### Find the middle term in the expansion of (x – 1/x)2n+1

Find the middle term in the expansion of $$(x-\dfrac{ 1}{x})^{2n+1}$$

#### Find the middle term in the expansion of (1 + 3x + 3x2 + x3)2n

Find the middle term in the expansion of (1 + 3x + 3x2 + x3)2n

Find the middle term in the expansion of $$(\dfrac{x}{a} – \dfrac{a}{x})^{10}$$