Find the Product:
\[ \left(3 + \frac{5}{x}\right) \left(9 – \frac{15}{x} + \frac{25}{x^2}\right) \]
Solution:
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=3,\qquad b=\frac{5}{x} \]
\[ \left(3 + \frac{5}{x}\right) \left(9 – \frac{15}{x} + \frac{25}{x^2}\right) \]
\[ = (3)^3 + \left(\frac{5}{x}\right)^3 \]
\[ = 27 + \frac{125}{x^3} \]