Determina el producto (x-y+1) ( x-y-1)

x^2 - 2xy + y^2 - 1

Explanation:

Let z = x-y

So we go from (x-y+1)(x-y-1) to (z+1)(z-1) after replacing "x-y" with "z"

Use the difference of squares rule to get (z+1)(z-1) = z^2 - 1

Now plug in z = x-y and expand using the FOIL rule

z^2 - 1 = (x-y)^2 - 1

z^2 - 1 = (x-y)(x-y) - 1

z^2 - 1 = x^2 - xy - yx + y^2 - 1

z^2 - 1 = x^2 - xy - xy + y^2 - 1

z^2 - 1 = x^2 - 2xy + y^2 - 1

Therefore, (x-y+1)(x-y-1) expands fully out to x^2 - 2xy + y^2 - 1