Disjunctive Normal Form
That looks good your original equation reduces to (bc' + bd') which is what you have put in your truth table and then extracted in DNF.

Edit to clarify reduction of original equation.

(a'+b) * (bc' + bd')= a'(bc' + bd')+b(bc' + bd')

              = a'(bc' + bd')+(bc' + bd')

              = (bc' + bd')