Advanced MathWhich one is a simplified expression for A(A'+B')(B+C)(B+C'+D)

Tazmin Horton

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

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)
=[+AB](B+C)(B+C+D)
Since PP=0
=[0+AB](B+C)(B+C+D)
=AB(B+C)(B+C+D)
Step 2
Multiply AB' with the terms in the first bracket of the obtained expression:
=[AB(B+C)](B+C+D)
=[ABB+ABC](B+C+D)
=[A(BB)+ABC](B+C+D)
Since PP=0
=[0+ABC](B+C+D)
=ABC(B+C+D)
Step 3
Multiply AB'C with all the terms in the bracket of the obtained expression:
=ABC(B+C+D)
=ABBC+ABCC+ABCD
=A(BB)C+AB(CC)+ABCD
Since PP=0
=0+0+ABCD
=ABCD
Thus the simplified expression is AB'CD.

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