Simplifying
(x + -1x2)(x2 + -1x)

Reorder the terms:
(x + -1x2)(-1x + x2)

Multiply (x + -1x2) * (-1x + x2)
(x(-1x + x2) + -1x2 * (-1x + x2))
((-1x * x + x2 * x) + -1x2 * (-1x + x2))
((-1x2 + x3) + -1x2 * (-1x + x2))
(-1x2 + x3 + (-1x * -1x2 + x2 * -1x2))
(-1x2 + x3 + (1x3 + -1x4))

Combine like terms: x3 + 1x3 = 2x3
(-1x2 + 2x3 + -1x4)