Factor completely u^2-16u+63

You could factor this in a few ways, but the easiest is trial and error. check out the products of 63 and see if you can find anything that adds up to - 16:

±63, ±1, ±7, ±9 ... the last two there could work. you know that you'll need two negatives to equal a positive 63, and - 7 + - 9 = - 16, so:

(y - 7) (x - 9) is your factorization.