factor (x-1)(x+2)^2-(x-1)^2(x+2)

Question

anonymous · Answer

Can anyone please help me factor the above problem?

jigglypuff314 · Answer

you can factor out what they have in common so (x-1)(x+2)^2-(x-1)^2(x+2)
                                                                      ((x-1)(x+2))((x+2)-(x-1))
then simplify                                                    ((x-1)(x+2))(x+2-x+1)
                                                                      ((x-1)(x+2))(3)
so                                                                   3(x-1)(x+2)

anonymous · Answer

What happens when you square the (x-1)

solomonzelman · Answer

x^2-2x+1

anonymous · Answer

But it should be (x-1)(x+1)

solomonzelman · Answer

(x-1) squared means 
(x-1)(x-1)

(x-1)(x+1) is a difference of perfect squares.
If you were to eliminate the middle term

solomonzelman · Answer

maybe it is not called that, but...
I get my point, right?

anonymous · Answer

Ok I gave it a shot.  I have to show each of the steps and not sure if I got it but I think I did.  
    Thanks to both of you for your help!!

solomonzelman · Answer

Will you be able to do these problems in the future?
just to make sure, do this one for me real quick.
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