I was doing this homework assignment and I was wondering if I am doing the corre

Question

I was doing this homework assignment and I was wondering if I am doing the correct steps. The direction says multiply out to obtain a sum of products.

The question is the following:

(a+b'c+d') (b'c+d'+e) (a+e') (ad+e')

The first thing I did was use the Distributive Law: X+YZ = (X+Y) (X+Z)

So I set X = b'c+d, Y = a , Z = e, thus I get the following:

( b'c+d' + ae ) (a+e') (ad+e')

Now I do the same law for the other half of the problem, setting X = e' , Y = a , and Z = ad.

So I get: ( b'c+d' + ae ) ( e' + aad ) which becomes ( b'c+d' + ae ) ( e' + ad ) since AA = A .

Now I multiply each term by each other and get this:

b'ce' + d'e' + aee' + adb'c' + add' + aade .

Using XX' = 0 and AA = A, it becomes the following:

b'ce' + d'e' + a + ab'c'd + a + ade

I notice there are two a in there, and that A + A = A so it becomes this then:

b'ce' + d'e' + ab'c'd + a + ade , which is my final answer.

I was wondering if I was doing it all correct or did I miss something?

Explanation / Answer

Given
y = (a+b'c+d)(b'c'+d'+e)(a+e')(ad+e')
y = (ab'c' + ad' + ae + b'cb'c' + b'cd' + b'ce)(aad + ae' + ade' + e'e')
y = (ab'c' + ad' + ae + 0 + b'cd' + b'ce)(ad + ae' + ade' + e')
y = (ab'c' + ad' + ae + b'cd' + b'ce)(ad + [a + ad + 1]e')
y = (ab'c' + ad' + ae + b'cd' + b'ce)(ad + e')
y = ab'c'ad + ab'c'e' + ad'ad + ad'e' + b'cd'ad + b'cd'e' + b'cead + b'cee'
y = ab'c'd + ab'c'e' + 0 + ad'e' + 0 + b'cd'e' + ab'cde + 0
y = ab'c'd + ab'c'e' + ad'e' + b'cd'e' + ab'cde
y = ab'd (c'+ce) + ab'c'e' + ad'e' + b'cd'e'
y = ab'd (c'+e) + ab'c'e' + ad'e' + b'cd'e' y = ab'dc'+ ab'de+ab'c'e' + ad'e' + b'cd'e'

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.