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Math Help - Expanding and then simplifying

  1. #1
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    Expanding and then simplifying

    Basically the question was in an exam I sat today, and it states

    Expand Fully and simplify:

    x(x-1)^2

    Basically everyone has a different answer, and so I was wondering if any of you could help me out? Thanks.
    Last edited by scotchegg; May 6th 2010 at 03:20 PM.
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  2. #2
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    Quote Originally Posted by scotchegg View Post
    Basically the question was in an exam I sat today, and it states

    Expand Fully and simplify:

    x(x-1)^2


    Basically everyone has a different answer, and so I was wondering if any of you could help me out? Thanks.
    x(x-1)^2 = x(x-1)(x-1) = x(x^2 -2x +1) = x^3 -2x^2 +x.
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  3. #3
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    Quote Originally Posted by Anonymous1 View Post
    x(x-1)^2 = x(x-1)(x-1) = x(x^2 -2x +1) = x^3 -2x^2 +x.
    But then it says to simplify? which is where everything falls apart... We got to the
    x^3 -2x^2 +x
    although can you simplify that?

    Or am I reading into the question too much?
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  4. #4
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    Quote Originally Posted by scotchegg View Post
    x^3 -2x^2 +x
    although can you simplify that?
    There are no like terms here, therefore you cannot simplify it any further.
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  5. #5
    Super Member Anonymous1's Avatar
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    I think your teachers thought process was...

    x(x-1)^2

    = x(x-1)(x-1) expanded

    = x(x^2 -2x +1) fully expanded

    = x^3 -2x^2 +x simplified

    ...Which is poorly worded, but I'm going to go out on a limb and guess he wasn't an english major.
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  6. #6
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    is the final answer
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  7. #7
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    One of my friends got the answer

    = x^3 -2x^2 +x
    = (x^2 - x)(x - 1)

    Trying to convince him that it is wrong, but im not sure...
    Plus the teacher wont give us the test back until at least next Friday as we were the first class to sit the test...

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  8. #8
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by scotchegg View Post
    One of my friends got the answer

    = x^3 -2x^2 +x
    = (x^2 - x)(x - 1)

    Trying to convince him that it is wrong, but im not sure...
    Plus the teacher wont give us the test back until at least next Friday as we were the first class to sit the test...

    Yes,

    x^3 -2x^2 + x = (x^2 - x)(x - 1)

    It's going to come down to semantics. I don't know why your teacher would say "simplify" when he meant "factor," though.
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  9. #9
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    Quote Originally Posted by Anonymous1 View Post
    Yes,

    x^3 -2x^2 + x = (x^2 - x)(x - 1)

    It's going to come down to semantics. I don't know why your teacher would say "simplify" when he meant "factor," though.
    Our teachers never make up good tests, so this one will probably be a very awkward question for them!

    Thanks to everyone that contributed, roll on results day...
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