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  1. #1
    Aut Vincere Aut Mori Snuffleupagus's Avatar
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    Dumb Math Question (no...really...it's dumb)

    So yeah, I didn't pay attention in school, and now I'm self teaching. My math book gives me this equation:

    (y/2+z/3) * (y/2+z/3)

    My logic is as follows:

    y/2*y/2=y^2/4

    y/2*z/3=yz/6

    z/3*z/3= z^2/9

    So my mid point is y^2/4 + yz/6 + yz/6 + z^2/9

    Which simplifies to y^2/4 + yz/3 + z^2/9

    My book OTOH tells me that the equation simplifies to y^2/4 + y^z/3 + z^2/9

    Plugging in numbers for the variables leads me to...frustration I just need a brief explanation as to why the problem simplifies as it does.

    Danke.

  2. #2
    riding once again jschen's Avatar
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    Your book evidently has a typo.
    If you notice this notice then you will notice that this notice is not worth noticing.

  3. #3
    Aut Vincere Aut Mori Snuffleupagus's Avatar
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    So my answer of y^2/4 + yz/3 + z^2/9 is correct given a problem of (y/2+z/3) * (y/2+z/3) I take it?

  4. #4
    commuter all star peregrine's Avatar
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    Hmmm I got the same result you did. Are you sure it could not be a typo?

  5. #5
    riding once again jschen's Avatar
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    Snuffleupagus, your answer is correct, and more importantly, your reasoning is sound.
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  6. #6
    SERENITY NOW!!! jyossarian's Avatar
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    Your answer looks right to me. You wouldn't raise y to the z power in that instance.
    HHCMF - Take pride in your ability to amaze lesser mortals! - MikeR



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  7. #7
    Aut Vincere Aut Mori Snuffleupagus's Avatar
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    Thanks for the help!

    Now back to work...

  8. #8
    No Rocket Surgeon eubi's Avatar
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    Wrong answers in the book can be very frustrating.

    Be sure you point it out to your professor/teacher. I had one professor that gave extra points if you caught an error in the book!

    You will get to the point that you are so confident in your answers, if the book has a different answer than you do, you will always believe the BOOK is wrong.

    Then you will get your degree.

    Now for some math fun. You are correct,

    (a+b)^2 = a^2 + 2ab + b^2

    Are you familiar with Pascal's triangle? The sum of the two numbers on the row above equals the number between those two numbers below. It relates to the problem you solved. It looks like this:

    ____1
    __1 2 1
    _1 3 3 1
    1 4 6 4 1
    etc...

    As we found before: (a+b)^2 = a^2 + 2ab + b^2. Note the coefficients of each term are
    1,2,1. The same as the second row in the triangle. Now watch this:

    (a+b)^3 = a^2 + 3(a^2)b + 3 a(b^2)+b^3. The coefficients of each term are now
    1,3,3,1. The same as the third row in the triangle!

    And so on, for any power of any binomial.

    This may save you some time during a test some day.

  9. #9
    SERENITY NOW!!! jyossarian's Avatar
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    Quote Originally Posted by eubi
    (a+b)^3 = a^3 + 3(a^2)b + 3 a(b^2)+b^3. The coefficients of each term are now
    1,3,3,1. The same as the third row in the triangle!
    Fixed
    HHCMF - Take pride in your ability to amaze lesser mortals! - MikeR



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  10. #10
    riding once again jschen's Avatar
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    Quote Originally Posted by eubi
    You will get to the point that you are so confident in your answers, if the book has a different answer than you do, you will always believe the BOOK is wrong.
    ...after verifying that the book's answer isn't (a) an equivalent answer expressed in a different form or (b) an alternative answer when asked to only look for one answer but when multiple answers exist.

    You will also develop a sense for "reasonableness" of answers. In your original post, the book's answer was clearly wrong. The thing that took any time at all to determine was whether your answer was correct.

    Quote Originally Posted by eubi
    Are you familiar with Pascal's triangle? The sum of the two numbers on the row above equals the number between those two numbers below. It relates to the problem you solved. It looks like this:

    ____1
    ___1 1
    __1 2 1
    _1 3 3 1
    1 4 6 4 1
    etc...
    Pascal's triangle (slight correction above) is useful for a number of things. Including what eubi pointed out. Good stuff.
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  11. #11
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    Perhaps i'm missing something here (and most likely i am), but isn't the most simplified version of this:

    (yz/6)^2

    maybe i just don't understand exactly what they're looking for. or maybe my math is wrong. see what happens when you pick your college because they sent you a letter saying your SAT scores were high enough to get in? curse you UNO, curse you!
    Say a prayer for all your friends and lovers waiting,
    so sad and patient by your side.

    Say a prayer for all your dreams in need of saving;
    it only takes a day to turn the tide.

    -Grey Revell, Save a Prayercard for the Devilman

  12. #12
    SERENITY NOW!!! jyossarian's Avatar
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    Quote Originally Posted by Ubie
    Perhaps i'm missing something here (and most likely i am), but isn't the most simplified version of this:

    (yz/6)^2

    maybe i just don't understand exactly what they're looking for. or maybe my math is wrong. see what happens when you pick your college because they sent you a letter saying your SAT scores were high enough to get in? curse you UNO, curse you!
    No, you don't multiply the two expressions again, you add them. Hence it would be yz/6+yz/6 = 2yz/6 which simplifies to yz/3. Go find an 11th grader and (s)he'll explain it better.

    On paper it'd look something like this:

    (y/2 + z/3)*(y/2 + z/3)

    y^2/4
    blank blankyz/6
    blank blankyz/6
    blank blank blank blankz^2/9
    +__________________
    y^2/4 + 2yz/6 + z^2/9

    simplified: y^2/4 + yz/3 + z^2/9
    Last edited by jyossarian; 03-08-06 at 09:38 AM.
    HHCMF - Take pride in your ability to amaze lesser mortals! - MikeR



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  13. #13
    riding once again jschen's Avatar
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    Quote Originally Posted by Ubie
    Perhaps i'm missing something here (and most likely i am), but isn't the most simplified version of this:

    (yz/6)^2

    maybe i just don't understand exactly what they're looking for. or maybe my math is wrong. see what happens when you pick your college because they sent you a letter saying your SAT scores were high enough to get in? curse you UNO, curse you!
    I think you looked at the original equation and accidently put in multiplication signs where the plus signs are.
    If you notice this notice then you will notice that this notice is not worth noticing.

  14. #14
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    Quote Originally Posted by jyossarian
    No, you don't multiply the two expressions again, you add them. Hence it would be yz/6+yz/6 = 2yz/6 which simplifies to yz/3. Go find an 11th grader and (s)he'll explain it better.

    On paper it'd look something like this:

    (y/2 + z/3)*(y/2 + z/3)

    y^2/4
    blank blankyz/6
    blank blankyz/6
    blank blank blank blankz^2/9
    +__________________
    y^2/4 + 2yz/6 + z^2/9

    simplified: y^2/4 + yz/3 + z^2/9
    d'oh! you're right!

    ***edit, everything i had entered is wrong, trying again below***

    so, the most simplified, straightforward thing i can come up with is:

    ((3y+2z)/6)^2
    Last edited by Ubie; 03-08-06 at 10:03 AM.
    Say a prayer for all your friends and lovers waiting,
    so sad and patient by your side.

    Say a prayer for all your dreams in need of saving;
    it only takes a day to turn the tide.

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  15. #15
    Aut Vincere Aut Mori Snuffleupagus's Avatar
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    Good reading.

    Bikeforums...one thousand one uses and counting

  16. #16
    No Rocket Surgeon eubi's Avatar
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    Quote Originally Posted by eubi
    (a+b)^3 = a^3 + 3(a^2)b + 3 a(b^2)+b^3.
    Argh!

    What I get for trying to teach math during break!

    Good catch jyossarian!

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