Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 27

$$4096p^6-6144p^5q+3840p^4q^2-1280p^3q^3+240p^2q^4-24pq^5+q^6$$

We know from the Binomial Theorem (page 693) that we can expand the given expression without multiplying it out. Doing this, we obtain: $$4096p^6-6144p^5q+3840p^4q^2-1280p^3q^3+240p^2q^4-24pq^5+q^6$$