I am struggling to prove which of these two terms is bigger in magnitude.
Assumption: \begin{align} A < \theta \end{align}
Term 1: \begin{align} \sqrt{\delta^2 \theta^4 + 4 \theta^2 A (\epsilon - 1 ) (1 + \varphi)} - \sqrt{\delta^2 \theta^2 A^2 + 4 \theta A^2 (\epsilon - 1 ) (1 + \varphi)} \end{align}
Term 2: \begin{align} \delta \theta A - \delta \theta^2 \end{align}
Signs of the coefficients: All coefficients are positive and $\epsilon > 1$.
My attempt: I have noticed that if we ignore the second term under the square roots Term 1 is the negative of Term 2. So I have tried to work with inequalities but I was unsuccessful. Does anyone have any ideas how to tackle this?