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u^2 + uv + v has no simple factorisation.
As a quadratic in u, it can be "factorised" by using the quadratic formula to find the root values (r1 and r2) for u, and then the factorisation would be (u - r1)(u - r2); however the values of the roots are:
r1 = (-v + √(v^2 - 4v))/2
r2 = (-v - √(v^2 - 4v))/2
which leads to the complicated "factorisation":
u^2 + uv + v = (u + (v + √(v^2 - 4v))/2)(u + (v - √(v^2 - 4v))/2)
What else can I help you with?
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