First, I factored the A out:
Now I am stuck. Any suggestion on the next step to take?
The word 'simplify' is especially not well defined for Boolean Algebra. The questions should be of the form prove one expression is another. Certain awful looking expressions in minterm expansion look compact in the maxterm expansions.
A(B'+C') + AB'D = AB'(1 + D) + AC' = AB' + AC' = A(B'+C') = A(BC)' = (A' + BC)'
You see, all the three expressions (namely A(B'+C'), A(BC)', (A' + BC)' ) are equal. So how do we decide which is "simple"?