Im trying to simplify the next expression
$$A\bar{B}E+\bar{A}B\bar{E}$$
so the approach is to factor $E$ and ·$\bar{E}$
to get something like
$$A\bar{B}+\bar{A}B (E+\bar{E})$$
(this step before is not allowed, so how to get last one?)
$$A\bar{B}+\bar{A}B (1)$$
and finally
$$A\bar{B}+\bar{A}B$$
but how can factor $E$ and their negation?
Going from:
$AB'E+A'BE'$
To:
$(AB'+A'B)(E +E')$
is not correct.
That is like going from
$2\cdot 3 \cdot 5+4\cdot 7\cdot 6$
To:
$(2\cdot 3+4 \cdot 7)(5 +6)$
which you can easily verify are not the same!
And indeed, with $A=T$, $B=F$, and $E=F$, we have that
$AB'E+A'BE'=TTF+FFT=F+F=F$
But
$(AB'+A'B)(E+E')=(T+F)(F+T)=TT=T$
So, these two are not equivalent!