Boolean Algebra

Question

can anyone explain why answer is different using a different sequence of steps? Although there no violation of priority order.

I think the answer should be same?

If any mistake please let me know. 

Comments

both answer are equivalent...

left one is ~a + ~b~z + ~b~x.....

right one is ~a + ~b~z + a~b~x , now use  a+bc = (a+b)(a+c) on bolded terms

(~a + a)(~a + ~b~x) = ~a + ~b~x....

Answer 1

You got simplified expression at right as

A'+B'Z'+AB'X'

Now apply distributive property

(A'+A)(A'+B'X')+B'Z'  ((A'+A)==1)

A'+B'X'+B'Z" == Left Side of Equation

Answer 2

Both equation is same because:

A'+B'Z'+AB'X' =B'Z'+(A'+B'X')(A'+A)  (Distributive property  A+BC=(A+B)(A+C))

hence   A'+B'Z'+B'X'