boolean algebra and simplify boolean expression

Question

question1:
from =$ab+ac+a'b'c$ , can I change it to $ab+b'c$ ?

=$ab+ac+a'b'c$
=$c.!(a+a'b')+ab$ -> applied demorgan, am I right?
=$c(a'.(a+b))+ab$
$c(a'a+a'b)+ab$
$a'bc+ab$
$b(a'c+a)$ ->should I apply demorgan again? , but after I apply it, I didn't get $ab+b'c$
is this true??

question 2:
Boolean algebra :

=$AB+A'B+AB'$ =A(B+B')+B(A+A') -> why $A'B$ changed to B(A+A') , what law is this?

Answer 1

Hints:

Question $1$: Note we can write $ac +a’b’c =c(a+a’b’)$. Now use absorption law.

Question $2$: Note that $AB+A’B+AB’=AB+AB+A’B+AB’=A(B+B’)+B(A+A’)$.