Factoring, Check my work, in a desperate struggle for life?

Question

Okay, this is the part 2, Sorry im new here anyways,

Let x^2 be x square

Given: (x-y)^2-(x-z)^2

work: [(x-y)(x-z)][(x-y)-x+z]
1) (2x-y-z)(-y+z)


My Final Anwser: -(2x-y-z)(y+z)

correct anwser: -(2x-y-z)(y-z)

Whats the big idea, where did I go wrong? why?

Answer 1

(x-y)²-(x-z)²

This is a difference of squares, and can be factored as such:

((x-y)+(x-z))((x-y)-(x-z))

Simplifying:

(x-y+x-z)(x-y-x+z)
(2x-y-z)(-y+z)
-(2x-y-z)(y-z)

Since you got (2x-y-z)(-y+z), it looks like the place where you made a mistake was in extracting the factor of -1 from the expression -y+z. Remember, the negative sign only applies to the y -- i.e. -y+z≠-(y+z).

Answer 2

You can expand:
[(x-y)-(x-z)][(x-y)+(x-z)]
(-y+z)(2x-y-z).
If you factor out a -1, you get
-(y-z)(2x-y-z)