What do you mean by a correct expression and what can you use in a proof? Can you use truth tables?
Working on the right-hand side,
\begin{align*}
xyz+wy'(x+z')&= xyz+wxy'+wy'z'\\ &=xyz+wxy'(z+z')+wy'z'\\ &=xyz+wxy'z+wxy'z'+wy'z'.
\end{align*}
Now, working on the left-hand side,
\begin{align*}
wxy'z'+xyz+wy'z'+wxz &=wxy'z'+xyz+wy'z'+wx(y+y')z\\ &=wxy'z'+xyz+wy'z'+wxyz+wxy'z\\ &=wxy'z'+xyz(1+w)+wy'z'+wxy'z\\ &=wxy'z'+xyz+wy'z'+wxy'z
\end{align*}