Simplifying
(x + -1y)(x + y)

Multiply (x + -1y) * (x + y)
(x(x + y) + -1y * (x + y))
((x * x + y * x) + -1y * (x + y))

Reorder the terms:
((xy + x2) + -1y * (x + y))
((xy + x2) + -1y * (x + y))
(xy + x2 + (x * -1y + y * -1y))
(xy + x2 + (-1xy + -1y2))

Reorder the terms:
(xy + -1xy + x2 + -1y2)

Combine like terms: xy + -1xy = 0
(0 + x2 + -1y2)
(x2 + -1y2)