  In this paper, utilizing Nevanlinna theory, we study existence and forms of
the entire solutions $ f $ of the quadratic trinomial-type partial
differential-difference equations in $ \mathbb{C}^n $
  \begin{align*}
  a\left(\alpha\dfrac{\partial f(z)}{\partial z_i} + \beta\dfrac{\partial
f(z)}{\partial z_j}\right)^2 + 2 \omega \left(\alpha\dfrac{\partial
f(z)}{\partial z_i} + \beta\dfrac{\partial f(z)}{\partial z_j}\right) f(z + c)
+ b f(z + c)^2 = e^{g(z)}
  \end{align*} and
  \begin{align*}
  a\left(\alpha\dfrac{\partial f(z)}{\partial z_i} + \beta\dfrac{\partial
f(z)}{\partial z_j}\right)^2 & + 2 \omega \left(\alpha\dfrac{\partial
f(z)}{\partial z_i} + \beta\dfrac{\partial f(z)}{\partial z_j}\right)
\Delta_cf(z) + b [\Delta_cf(z)]^2 = e^{g(z)},
  \end{align*} where $ a, \omega, b\in\mathbb{C} $, $ g $ is a polynomial in $
\mathbb{C}^n $ and $ \Delta_cf(z)=f(z+c)-f(z) $. The main results of the paper
improve several existence results in $ \mathbb{C}^n $ for integer $ n\geq 2 $
and $ 1\leq i<j\leq n $ and their corollaries of the paper are an extension of
the results of Xu \emph{et al. } for trinomial equation with arbitrary
coefficient in $ \mathbb{C}^2 $. Moreover, examples are exhibited to validate
the conclusion of the main results.
