Question

Expand the expression \((x+ \frac{1}{x})^6\).

Answer 1

By using Binomial Theorem, the expression \((x+ \frac{1}{x})^6\) can be expanded as

\((x+ \frac{1}{x})^6\) = \(^6C_0 (x)^6 + ^6C_1(x)^5(\frac{1}{x}) + ^6C_2(x)^4(\frac{1}{x}) + ^6C_3(x)^3(\frac{1}{x})^3 + ^6C_4(x)^2(\frac{1}{x})^4 +\)\( ^6C_5(x)(\frac{1}{x})^5 + ^6C_6(\frac{1}{x})^6\)

=\(x^6 + 6(x)^5(\frac{1}{x}) + 15(x)^4(\frac{1}{x^2}) + 20(x)^3(\frac{1}{x^3}) + 15 (x)^2 (\frac{1}{x^4}) + 6(x)(\frac{1}{x^5}) + \frac{1}{ x^6}\)

=\(x^6 + 6x^4 + 15x^2 + 20+ \frac{15}{x^2} + \frac{6}{x^4} + \frac{1}{ x^6}\)