• # question_answer The 4th term from the end in the expansion of${{\left( \mathbf{x}+\frac{2}{x} \right)}^{9}}$ A) $\frac{5376}{{{x}^{4}}}$                  B) $\frac{{{x}^{3}}}{5376}$C) $\frac{5376}{{{x}^{3}}}$                              D) $\frac{{{x}^{4}}}{5376}$

[c] 4th term from the end of the expansion of ${{\left( x+\frac{2}{x} \right)}^{9}}$ ${{=}^{9}}{{C}_{3}}.{{\left( \frac{2}{x} \right)}^{6}}{{(x)}^{3}}{{=}^{9}}{{C}_{3}}\times \frac{{{\left( 2 \right)}^{6}}}{{{(x)}^{3}}}=\frac{\frac{9\times 8\times 7}{3\times 2}\times 64}{{{x}^{3}}}=\frac{168\times 32}{{{x}^{3}}}=\frac{5356}{{{x}^{3}}\,.}$