Simplify to obtain a sum of products: (a+b)(c+b)(d? +b)(acd? +e)

(ACD'+BE)

Explanation:

(A+B)(C+B)(D'+B)(ACD'+E)

Product of (A+B)(C+B)

(A+B)(C+B)=AC+AB+BC+B^2 = AC+B(A+C+B)=AC+B

Product of (D'+B)(ACD'+E) with AC+B

(AC+B)(D'+B)(ACD'+E)

(AC+B)(D'+B)=ACD' + ACB +BD +B = ACD'+B(AC+D+1)=ACD'+B

Then we get:

(ACD'+B)(ACD'+E) = ACD'+ACD'E+ACD'B+BE

ACD'(1+E+B)+BE =ACD'+BE

the answer is gallery.