Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 34

-13608

We know from the Binomial Theorem (page 693) that we can expand the given expression without multiplying it out. Doing this, we obtain: $$x^{16}-24x^{14}+252x^{12}-1512x^{10}+5670x^8-13608x^6+20412x^4-17496x^2+6561$$ Thus, the given coefficient is -13608.