How can this be distributed A U B Intersection C U B or A U

How can this be distributed? (A U B) Intersection (C U B)

or (A U B) U (C Intersection B)

or Any problem that goes similar to what you would FOIL in other examples in general?

(eg. Format (Set 1 Operation Set 2) operation (Set 2 Operation Set 3) )

First let\'s understand this with taking simple example

R(ST)=(RS)(RT)

As you see above how union is distributed over intersection

Now applying same rule for your asked format,

(Set1 Operation1 Set2) OPERATION (Set3 Operation2 Set4)=((Set1 Operation1 Set2) OPERATION Set3) Operation2 ((Set1 Operation1 Set2) OPERATION Set4)

Applying this in (AB)(CB)=((AB)C)((AB)B)=(ABC)(AB)

Similarly for (AB)(CB)=((AB)C)((AB)B)=(ABC)(AB)