Chapter 11.4, Problem 52E

Exercises 50-52 will help you prepare for the material covered in the next section. Each exercise involves observing a pattern in the expanded form of the binomial expression ${(a+b)}^n$.

$\begin{array}{l}{(}^a=a+b\\ {(}^a=a^{2}2ab+b^2\\ {(}^a=a^3+3a^{2}b+3a{b}^2+b^3\\ {(}^a=a^4+4a^{3}b+6a^2{b}^2+4a{b}^3+b_4\\ {(}^a=a^5+5a^{4}b+10a^3{b}^2+10a^2{b}^3+\end{array}$

Describe the pattern for the sum of the exponents on the variables in each term.