Multiply out and simplify to obtain a minimum sum-of-products boolean expression:

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

As per the question, we need to convert product of sum into sum of product,

Given:

(A' + B+C') (A'+C'+D) (B'+D'),

At first, we will solve to parenthesis,

= (A'+C'+BD) (B'+D')

As per the Rule, (A+B) (A+C) = A+BC, In our case if we assume X = A'+C', then,

(A' + B+C') (A'+C'+D) = (A'+C'+B) (A'+C'+D) = (A'+C'+BD)

Now,

= (A'+C'+BD) (B'+D') = A'B' + A'D' + C'B' + C'D' + BDB' + BDD"

As we know that AA' = 0, it mean

=A'B'+A'D'+C'B'+C'D'+D*0+B0

=A'B'+A'D'+C'B'+C'D' as B * 0 and D*0 = 0

Finally, minimum sum of product boolean expression is

A''B'+A'D'+C'B'+C'D'

=