Factor By grouping.
(u + v)x - xy + (u + v)^2 - (u + v)y
(u + v)[x - xy + (u + v) - y]
(u + v)[x (1 - y) + (u + v) - y]
Is this correct?
No.
The first pair share an x, so
(u + v)x - xy = x[(u + v) - y].
The second pair share (u + v), so
(u + v)^2 - (u + v)y = (u + v)[(u + v) - y].
Putting those together, you have
(u + v)x - xy + (u + v)^2 - (u + v)y =
x[(u + v) - y] + (u + v)[(u + v) - y] =
x(u + v - y) + (u + v)(u + v - y)
What can you factor out next?