I know that $x = y + \mathcal{O}(\eta^3)$. However, I also know that $\eta = \gamma + \mathcal{O}(\delta^2)$. What is the order of $x$?
My guess is that since $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ we should have something like $$ x = y + \mathcal{O}((\gamma + \mathcal{O}(\delta^2))^3) \approx y + \mathcal{O}(\gamma^3) + \mathcal{O}(\gamma^2\delta^2) + \mathcal{O}(\gamma \delta^4) + \mathcal{O}(\delta^6) \approx y + \mathcal{O}(\delta^2) $$ Is that correct?