multiplying Big O $\left(x^3+2x^2+O\left(x\right)\right)\cdot \left(1+\frac{1}{x}+O\left(\frac{1}{x^2}\right)\right)$

Question

multiplying I reach to this result $x^3+3x^2+2x+O\left(x\right)+O\left(1\right)$

that is not right answer

Answer 1

You don't specify whether $x \to 0$ or $x \to \infty$.

This is an odd question since the first term is of the form usually associated with $x \to 0$ and the second with $x \to \infty$.

So, until you tell us which holds, there is no way to answer this question.