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<p>In the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$, the sum of coefficients of each term is $992$ more than the sum of the binomial coefficients, $\left( \begin{matrix}
   n  \\
   r  \\
\end{matrix} \right)$, where&nbsp;$r=0,\,\,1,\,\,2,\,\,\ldots ,\,\,n$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the value of $n$</div></li><li><div class="list-item-paragraph">Hence find the term with the greatest coefficient in the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$.</div></li></ol>

In the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$, the sum of coefficients of each term is $992$ more than the sum of the binomial coefficients, $\left( \begin{matrix}
   n  \\
   r  \\
\end{matrix} \right)$, where $r=0,\,\,1,\,\,2,\,\,\ldots ,\,\,n$.

Sums of Coefficients in Polynomial Expansions

Finding Parameters in Binomial Expansions

Greatest Coefficients in Binomial Expansions

Binomial Theorem

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