Convert Expression to Sum of Prod & Prod of Sums

[fend]

Homework Statement

Convert the following expression into sum of products and products of sums

(AB+C)(B+C'D)

Homework Equations

Distributive Property

The Attempt at a Solution

for product of sums it would be (AB+C)(B+C'D) since it is already in this form.

When calculating sum of products I get...
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
= A*1+ABC'D+CB = A+ABC'D+CB (this is where I get confused)
=A(1+BC'D)+CB
(I know 1+X=1 but what about 1+BC'D? Can I reduce this further of would A(1+BC'D)+CB be in the correct form?)

 

[vela]

Homework Statement

Convert the following expression into sum of products and products of sums

(AB+C)(B+C'D)

Homework Equations

Distributive Property

The Attempt at a Solution

for product of sums it would be (AB+C)(B+C'D) since it is already in this form.

That's not a product of sums. You can't have products like AB in the expression.

When calculating sum of products I get...
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
= A*1+ABC'D+CB = A+ABC'D+CB (this is where I get confused)
=A(1+BC'D)+CB
(I know 1+X=1 but what about 1+BC'D? Can I reduce this further of would A(1+BC'D)+CB be in the correct form?)

ABB ≠ A. Evaluate both sides with A=1 and B=0, for instance.

 

[fend]

sum of products
Oh yes I see!
(AB+C)(B+C'D) = ABB+ABC'D+CB+CC'D = ABB+ABC'D+CB+0D = ABB+ABC'D+CB
=AB+ABC'D+CB
Then this would be in the correct form!