Question

Factor by grouping. x2 + 8x + xy + 8y

Answer 1

Don't you see that y is a stranger. So group it -y(x+8) 
The balance just happens to be x(x+8) 
So you have these two terms. Take the common factor out. 
(x+8) (x-y) now that's the answer. Easy ... 

Answer 2

= x(x + 8) - y(x + 8)
= (x - y)(x + 8)