factorize :x2-2X+xy-2y

x(x-2) + y(x-2)

(x+y)(x-2)

To factorize the expression x^2 - 2x + xy - 2y, we can group the terms separately and factor them individually.

First, let's group the terms with x together and the terms with y together:

x^2 - 2x + xy - 2y

= (x^2 - 2x) + (xy - 2y)

Now, let's factor out the common terms from each group:

x(x - 2) + y(x - 2)

Notice that both terms in each group share a common factor of (x - 2). We can factor out (x - 2) from both terms:

(x - 2)(x + y)

Hence, the factored form of the expression x^2 - 2x + xy - 2y is (x - 2)(x + y).