Answer
$a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6$
Work Step by Step
The coefficients in the the $n=
6
$ row of Pascal's Triangle are $\{
1,6,15,20,15,6,1
\}$. Using these as the coefficients of the terms that follow the pattern in expanding binomials, the expression $
(a+b)^6
$ expands to
\begin{array}{l}
a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6
.\end{array}
