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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Expand each of the expressions:$\big(\large\frac{2}{x}-\frac{x}{2}\big)^5$

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Toolbox:
  • $(a-b)^n=nC_0a^n-nC_1a^{n-1}b+nC_2a^{n-2}b^2.......+(-1)^nnC_ra^{n-r}b^r+......nC_n(-b)^n$
$\big(\large\frac{2}{x}-\frac{x}{2}\big)^5$
$\Rightarrow C(5,0)(\large\frac{2}{x})^5$$+C(5,1)(\large\frac{2}{x})^4(-\frac{x}{2})$$+C(5,2)(\large\frac{2}{x})^3(\frac{-x}{2})^2$$+C(5,3)(\large\frac{2}{x})^2(\frac{-x}{2})^3$$+C(5,4)(\large\frac{2}{x})(\frac{x}{4})^4$$+C(5,5)(\large\frac{-x}{2})^5$
$\Rightarrow 1(\large\frac{2}{x})^5$$+5(\large\frac{2}{x})^4(-\frac{x}{2})$$+10(\large\frac{2}{x})^3(\frac{-x}{2})^2$$+10(\large\frac{2}{x})^2(\frac{-x}{2})^3$$+5(\large\frac{2}{x})(\frac{-x}{2})^4$$+(\large\frac{x}{2})^5$
$\Rightarrow 32x^{-5}-40 x^{-3}+20x^{-1}-5x+\large\frac{5}{8}$$x^3-\large\frac{1}{32}$$x^5$
answered Jun 20, 2014 by sreemathi.v
 
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