SOLUTION: Hi, I would like help in solving this question: (x-1)(x-2)^2 - (x-1)^2 (x-2) I don't really know where to start, but I started to foil and don't know where i ended up at.

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Hi, I would like help in solving this question: (x-1)(x-2)^2 - (x-1)^2 (x-2) I don't really know where to start, but I started to foil and don't know where i ended up at.      Log On


   

Question 635003: Hi, I would like help in solving this question:
(x-1)(x-2)^2 - (x-1)^2 (x-2)
I don't really know where to start, but I started to foil and don't know where i ended up at.
Found 2 solutions by lwsshak3, Maths68:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
simplify
(x-1)(x-2)^2 - (x-1)^2 (x-2)
factor out (x-1)(x-2)
(x-1)(x-2)[(x-2)-(x-1)]
=(x-1)(x-2)[(x-2-x+1)]
=(x-1)(x-2)(-1)
=-(x-1)(x-2)

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
=%28x-1%29%28x-2%29%28%28x-2%29+-+%28x-1%29%29
=%28x-1%29%28x-2%29%28x-2-x%2B1%29
=%28x-1%29%28x-2%29%28cross%28x%29-2-cross%28x%29%2B1%29
=%28x-1%29%28x-2%29%28-1%29
=%28x-1%29%28x-2%29%28-1%29
=%28x%28x-2%29-1%28x-2%29%29%28-1%29
=%28x%5E2-2x-1x%2B2%29%28-1%29
=%28x%5E2-3x%2B2%29%28-1%29
=-x%5E2%2B3x-2


OR


=%28x-1%29%28x-2%29%5E2+-+%28x-1%29%5E2+%28x-2%29
=%28x-1%29%28x%5E2-4x%2B2%5E2%29+-+%28x%5E2-2x%2B1%5E2%29%28x-2%29
=%28x-1%29%28x%5E2-4x%2B4%29+-+%28x%5E2-2x%2B1%29%28x-2%29
=%28x%28x%5E2-4x%2B4%29-1%28x%5E2-4x%2B4%29%29+-%28x%28x%5E2-2x%2B1%29-2%28x%5E2-2x%2B1%29%29
=%28x%5E3-4x%5E2%2B4x-x%5E2%2B4x-4%29+-++%28x%5E3-2x%5E2%2Bx-2x%5E2%2B4x-2%29
=%28x%5E3-4x%5E2-x%5E2%2B4x%2B4x-4%29+-++%28x%5E3-2x%5E2-2x%5E2%2Bx%2B4x-2%29
=%28x%5E3-5x%5E2%2B8x-4%29+-++%28x%5E3-4x%5E2%2B5x-2%29
=x%5E3-x%5E3-5x%5E2%2B4x%5E2%2B8x-5x-4%2B2
=cross%28x%5E3%29-cross%28x%5E3%29-x%5E2%2B3x-2
=-x%5E2%2B3x-2