Question

1+p+q+r+pq+qr+pr+pqr​

Answer 1

Answer:

The answer is (p+1)(q+1)(r+1)

Step-by-step explanation:

=>1+p+q+r+pq+qr+pr+pqr

Do the grouping 1+p+q+r+pq+qr+pr+pqr=(pqr+pq+pr+p)+(qr+q+r+1), and factor out p in pqr+pq+pr+p.

=>p(qr+q+r+1)+qr+q+r+1

Factor out common term qr+q+r+1 by using distributive property.

=>(qr+q+r+1)(p+1)

Consider qr+q+r+1. Do the grouping qr+q+r+1=(qr+q)+(r+1), and factor out q in qr+q.

=>q(r+1)+r+1

Factor out common term r+1 by using distributive property.

=>(r+1)(q+1)

Rewrite the complete factored expression.

=>(p+1)(q+1)(r+1)

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