Elementary Technical Mathematics

$x^2 - y^2- 5x+5y$
We multiply each term of the first polynomial by each term of the second polynomial as follows: $$(x + y - 5)(x- y)=x (x- y)+ y(x- y) - 5(x- y)\\ =x^2 -x y+ yx- y^2- 5x+5y\\ =x^2 - y^2- 5x+5y .$$