Did I simplify the boolean expression correctly?

Question

I wanted someone to check and make sure that I did this right, I'm hoping that I did but if I didn't, please point me in the right direction of where I went wrong

Answer 1

$\begin{align}&\rm y(x'z+xz')+x(yz+yz') \\ =\quad &\rm y(x'z+xz')+xy(z+z')&& \text{Distribution} \\ =\quad &\rm y(x'z+xz')+xy(1)&& \text{Complementation (/Inversion)} \\ =\quad &\rm x'yz+xyz'+xy &&\text{Distribution and Identity.} \end{align}$

You were okay up to here, then you went all agley.   Instead, the next step should be to distribute out the $y$ factor.

$\begin{align}=\quad &\rm y(x'z+xz'+x) &&\text{Distribution} \end{align}$

From here your path to the destination should be obvious.