Answer
$4u^2v+uv^2$
Work Step by Step
Here, we have $\dfrac{\partial x}{\partial u}=2u+v$ and $\dfrac{\partial x}{\partial v}=u$
Also, $\dfrac{\partial y}{\partial u}=v^2$ and $\dfrac{\partial y}{\partial v}=2uv$
Now, $Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial u}&\dfrac{\partial x}{\partial v}\\\dfrac{\partial y}{\partial u}&\dfrac{\partial y}{\partial v}\end{vmatrix}=\begin{vmatrix} 2u+v&u\\v^2&2uv\end{vmatrix}=4u^2v+2uv^2-uv^2=4u^2v+uv^2$
