Please Help With Problem

P^2 q – pq^2 – rp^2 q + rpq^2

Solution

Answer: pq(1-r)(p-q)

Looking at the equation we can see “pq” in each term. Therefore we can factor it out first and get

pq(p-q-rp+rq)

Using the grouping method we can do

1(p-q) + r(-p+q)

If you notice (p-q) and (-p+q) are opposites so we can factor out a negative to get them to be the same

1(p-q) -r(p-q)

(1-r)(p-q)

bring back our pq term from earlier

pq(1-r)(p-q)