Answered: "Advanced MathWhich one is a simplified expression for..."

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Advanced Math
Upper Level Math

Tazmin Horton

Answered question

2021-02-05

Advanced Math
Which one is a simplified expression for $A (A^{'} + B^{'}) (B + C) (B + C^{'} + D)$

Answer & Explanation

Usamah Prosser

Skilled2021-02-06Added 86 answers

Step 1
Multiply A with the terms in the first bracket:
$= [A (A^{'} + B^{'})] (B + C) (B + C^{'} + D)$
$= [\forall^{'} + A B^{'}] (B + C) (B + C^{'} + D)$
Since $P P^{'} = 0$
$= [0 + A B^{'}] (B + C) (B + C^{'} + D)$
$= A B^{'} (B + C) (B + C^{'} + D)$
Step 2
Multiply AB' with the terms in the first bracket of the obtained expression:
$= [A B^{'} (B + C)] (B + C^{'} + D)$
$= [A B B^{'} + A B^{'} C] (B + C^{'} + D)$
$= [A (B B^{'}) + A B^{'} C] (B + C^{'} + D)$
Since $P P^{'} = 0$
$= [0 + A B^{'} C] (B + C^{'} + D)$
$= A B^{'} C (B + C^{'} + D)$
Step 3
Multiply AB'C with all the terms in the bracket of the obtained expression:
$= A B^{'} C (B + C^{'} + D)$
$= A B B^{'} C + A B^{'} C C^{'} + A B^{'} C D$
$= A (B B^{'}) C + A B^{'} (C C^{'}) + A B^{'} C D$
Since $P P^{'} = 0$
$= 0 + 0 + A B^{'} C D$
$= A B^{'} C D$
Thus the simplified expression is AB'CD.

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