The truth table of a full adder is as below.
Cout is given as Cout = AB + Cin(A XOR B).
not sure why is that because when I do my k-map on the Cout, I get Cout = AB + Cin(A+B).
does anyone know why is that?
If you drew up a truth table for the expression you found, you'd realise that it would exactly the same as the one for the expression they've given you (so you're not wrong). Since you would already have circuitry to find A XOR B (to find S), however, the output of the same circuitry should be re-used to find Cout as shown in the diagram below in order to save the extra space and transistors (or whatever hardware is being used) that would be required by an additional OR gate.
(Source: Wikimedia Commons)