Converting DNF to CNF (Boolean Logic)

Question

I've tried at least a dozen ways to convert this DNF to CNF, yet I always end up with something unusable.

Here is the DNF -> z:(C∧D∧B)∨(¬B∧¬C∧D)∨(¬D∧C)

I need to convert it mathematically (with clear logical steps)

Here is a similar problem with the type of answer I would need: Boolean Logic Converting DNF to CNF

Answer 1

HINT

Are you familiar with FOIL, that says that $(A+B)(C+D) = AC+AD+BC+BD$?

Well, that principle generalizes more larger or more terms, simply by systematically taking all possible ways of taking 1 member from each term. For example:

$(A+B + E)(C+D) = AC+AD+BC+BD + EC + ED$

or

$(A+B + E)(C+D + F) = AC+AD+AF+BC+BD + BF+EC + ED+EF$

or

$(A+B)(C+D)(E+f) = ACE+ACF+ADE+ADF+BCE+BCF+BDE+BDF$

See how this works? With conjunctions of disjunctions (or vice versa) you can do the exact same thing.