Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 22

$$a^8+8a^7b^2+28a^6b^4+56a^5b^6+70a^4b^8+56a^3b^{10}+28a^2b^{12}+8ab^{14}+b^{16}$$

We know from the Binomial Theorem (page 693) that we can expand the given expression using Pascal's Triangle. Doing this, we obtain: $$a^8+8a^7b^2+28a^6b^4+56a^5b^6+70a^4b^8+56a^3b^{10}+28a^2b^{12}+8ab^{14}+b^{16}$$