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Math Help - polynomial

  1. #1
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    polynomial

    I'm asked to simplify

    (x+2)^2 (x-1)^2 - (x-4)^2 (x+4)^2

    something is wrong with this x^2 +4x +4 +x^2 - 1 -x^2 +16 +x^2 +8x +16
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by reallylongnickname View Post
    I'm asked to simplify

    (x+2)^2 (x-1)^2 - (x-4)^2 (x+4)^2

    something is wrong with this x^2 +4x +4 +x^2 - 1 -x^2 +16 +x^2 +8x +16
    First, you are expanding out the individual terms, but you aren't multiplying them.

    (x^2 +4x +4) + (x^2 - 1) - (x^2 +16) + (x^2 +8x +16)

    Second you are not squaring these right.
    (x - 1)^2 = x^2 - 2x + 1, not x^2 -1

    -Dan
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  3. #3
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    Since a^2b^2 = (ab)^2 it can be rewritten as ((x+2)(x-1))^2 - ((x-4)(x+4))^2

    This gives an equation of the form a^2-b^2 so you can use the difference of two squares.

    An alternative method is the one highlighted above
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  4. #4
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    (x^2 +4x +4) (x^2 -2x -1) - (x^2 +16) (x^2 +8x +16)

    -x^2 -16 (x^2 +8x +16)

    -x^4 -8x^3 -16x^2 -16x^2 -128x -256

    x^4 -2x^3 -x^2 + 4x^3 -8x -4x +4x^2 -8x -4 -x^2 - 16 -x^4 -8x^3 -16x^2 -16x^2 -128x -256

    It's not finished yet I know. Once I started collecting like terms, I notice something was done wrong.
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  5. #5
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    Quote Originally Posted by reallylongnickname View Post
    (x^2 +4x +4) (x^2 -2x -1) - (x^2 +16) (x^2 +8x +16)
    (x-4)^2 isn't  (x^2+16) It is  x^2 - 8x +16
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  6. #6
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    For the 2nd part: -(x^2 -8x +16) (x^2 +8x +16)
    I came up with: -x^2 +8x -16 (x^2 +8x +16)
    then: -x^2 _8x^3 -16x^2 + 8x^3 + 64x^2 +128x -16^2 -128x -256

    Still doing something wrong.
    Last edited by reallylongnickname; March 19th 2011 at 04:23 PM.
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by reallylongnickname View Post
    For the 2nd part: -(x^2 -8x +16) (x^2 +8x +16)
    I came up with: -x^2 +8x -16 (x^2 +8x +16)
    then: -x^2 _8x^3 -16x^2 + 8x^3 + 64x^2 +128x -16^2 -128x -256

    Still doing something wrong.
    You have it. Just collect like terms.

    -Dan
    Last edited by mr fantastic; March 19th 2011 at 08:09 PM. Reason: Dealt with OP bumping.
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  8. #8
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    The answer I came up with is: 2x^3 +25x^2 -252 The correct answer is apparently:
    2x^3 +29x^2 -4x -252

    By the way, where does everyone get the application to nicely display math work like that?
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by reallylongnickname View Post
    The answer I came up with is: 2x^3 +25x^2 -252 The correct answer is apparently:
    2x^3 +29x^2 -4x -252

    By the way, where does everyone get the application to nicely display math work like that?
    Yes, that is correct!

    For the LaTeX codes, see here.

    -Dan
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