Hi
(u+1)(u+1) is a perfect square: would give us: u^2 + 2u + 1
Note: the sum of the Inner Product and Outer Product would yield the 2u needed
another example:
x^2 + 6x ... to end up to be a perfect square that would need to be x^2 +6x + 9
As x^2 + 6x + 9 is (x+3)(x+3)