Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 30

$$729u^6+1458u^5v^2+1215u^4v^4+540u^3v^6+135u^2v^8+18uv^{10}+v^{12}$$

We know from the Binomial Theorem (page 693) that we can expand the given expression without multiplying it out. Doing this, we obtain: $$729u^6+1458u^5v^2+1215u^4v^4+540u^3v^6+135u^2v^8+18uv^{10}+v^{12}$$