Find the Cube of the Following Binomial Expression
\[ 2x+\frac{3}{x} \]
Solution:
Using identity:
\[ (a+b)^3 = a^3+b^3+3ab(a+b) \]
\[ \left(2x+\frac{3}{x}\right)^3 \]
\[ = (2x)^3 + \left(\frac{3}{x}\right)^3 + 3(2x)\left(\frac{3}{x}\right) \left(2x+\frac{3}{x}\right) \]
\[ = 8x^3 + \frac{27}{x^3} + 18\left(2x+\frac{3}{x}\right) \]
\[ = 8x^3 + \frac{27}{x^3} + 36x + \frac{54}{x} \]