Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - 10.2 Exercises - Quiz for Lessons 10.1-10.2 - Page 697: 14

$$32x^{15}-240x^{12}y+720x^9y^2-1080x^6y^3+810x^3y^4-243y^5$$

We know from the Binomial Theorem (page 693) that we can expand the given expression without multiplying it out. Doing this, we obtain: $$32x^{15}-240x^{12}y+720x^9y^2-1080x^6y^3+810x^3y^4-243y^5$$