Give an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms [for example: -3x(2xy + 3y - 2x)] and show each step of the distribution. Why do you think many students make sign errors on this type of problem? What would be your advice to a student who has trouble with the signs?
(-3x)(2xy + 3y - 2x) =
(-3x)(2xy + 3y + (-2x)) =
(-3x)(2xy) + (-3x)(3y) + (-3x)(-2x) =
-6(x^2)y - 9xy + 6(x^2).
As for advice, just be careful that you reverse *every* sign when multiplying by a negative.
Also, some students find it easier to get the right answer if they always rewrite x - y as x + (-y).