I read this as u^2-26uv+120v^2. Write down all pairs of factors of 120:
(1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12)
Now write down the sums of these factors:
121, 62, 43, 34, 29, 26, 23, 22
We need the factors whose sum is 26, the coefficient of the middle term: (6,20). We have the solution:
(u-6v)(u-20v).