Completely factor the expression by grouping, if possible.
\[
q^{2}-q u-7 q+7 u
\]

Step 1 ：Rewrite the expression as a combination of two pairs of terms that have common factors. The first two terms have a common factor of q and the last two terms have a common factor of 7.

Step 2 ：Factor out these common factors from each pair of terms. This gives us the expression in the form of \(q(q - u) - 7(q - u)\).

Step 3 ：Notice that the expression now has a common factor of \(q - u\) in both terms. Factor out this common factor to get the completely factored form of the expression.

Step 4 ：The completely factored form of the expression \(q^{2}-q u-7 q+7 u\) by grouping is \(\boxed{(q - 7)(q - u)}\).