Answer
$q^7-7q^6r+21q^5r^2-35q^4r^3+35q^3r^4-21q^2r^5+7qr^6-r^7$
Work Step by Step
The coefficients in the the $n=
7
$ row of Pascal's Triangle are $\{
1,7,21,35,35,21,7,1
\}$. Using these as the coefficients of the terms that follow the pattern in expanding binomials, the expression $
(q-r)^7
$ expands to
\begin{array}{l}
q^7-7q^6r+21q^5r^2-35q^4r^3+35q^3r^4-21q^2r^5+7qr^6-r^7
.\end{array}
