By considering the general term in the binomial expansion of \({{\left( \frac{3}{{{x}^{5}}}-\frac{x}

Question

By considering the general term in the binomial expansion of ${{\left( \frac{3}{{{x}^{5}}}-\frac{x}{2} \right)}^{6}}$, explain why there are only two of non-negative powers of $x$ in this expansion. Find the term independent of $x$ in the expansion of $\left( 6-\frac{5}{{{x}^{2}}} \right){{\left( \frac{3}{{{x}^{5}}}-\frac{x}{2} \right)}^{6}}$.

Accepted Answer

(a) The only two non-negative powers are $0$ and $6$ (b) $ -\frac{27}{8}$

Binomial Theorem - Coefficients in Products of Binomial Expansions

Binomial Theorem - Coefficients in Products of Binomial Expansions

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