Question

How do you factor `2x - 2y - x² + 2xy - y²`?

Answer 1

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

Explanation:

We note that ;
`- x^2 + 2xy - y^2 = - (x^2 - 2xy + y^2) = - (x - y)^2`
Then, the expression transforms itself to:
`f(x,y) = 2(x - y) - (x - y)^2`
Put (x - y) into common factor -->
f(x,y) = (x -y)(2 - x + y)