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  4. The term independent of x in the expansion of (x - (1/x))4(x + (1/x))3 is

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Q. The term independent of $x$ in the expansion of $\left(x - \frac{1}{x}\right)^{4}\left(x + \frac{1}{x}\right)^{3}$ is

NTA AbhyasNTA Abhyas 2020Binomial Theorem

Solution:

$\left(x - \frac{1}{x}\right)\left(x - \frac{1}{x}\right)^{3}\left(x + \frac{1}{x}\right)^{3}$
$=\left(x - \frac{1}{x}\right)\left(x^{2} - \frac{1}{x^{2}}\right)^{3}$
$=\left(x - \frac{1}{x}\right)\left(x^{6} - 3 x^{2} + 3 \frac{1}{x^{2}} - \frac{1}{x^{6}}\right)$
There is no term containing $\frac{1}{x}$ and $x$ in the second bracket.
So, the expansion will not contain any term independent of $x$ .