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Homework Help: Simplifying an expression

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data

    I have a quiz tomorrow and i know a problem like this is gonna be on it and i need to figure out the process

    2. Relevant equations

    the expression is: [tex](2x^2-3x+1)(4)(3x+2)^3(3)+(3x+2)^4(4x-3)[/tex]

    3. The attempt at a solution

    i know the final answer[tex](3x+2)^3(36x^2-37x+6)[/tex]

    Ive tried to work the problem several times and i can't figure out how it turns out to be this. can somebody please do a step by step. it would be greatly appreciated.
     
  2. jcsd
  3. Feb 4, 2010 #2

    Mentallic

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    Homework Helper

    Sure thing. (by the way you should have called it factorizing an expression :tongue:)

    You need to have the basic idea of factorizing deeply embedded into your head. Mainly, [tex]ab+ac=a(b+c)[/tex] (1). a,b and c could be anything much more complicated.

    Lets take [tex]a=x^2(x+1)^2[/tex]

    Then we would need to factorize [tex]x^2(x+1)^2b+x^2(x+1)^2c[/tex]

    Can you now see how we can factorize out the a (or in this case the [tex]x^2(x+1)^2[/tex]) ? We now get the same thing as in (1): [tex]a(b+c)=x^2(x+1)^2(b+c)[/tex]

    At the same time, b and c can be something more complicated as well. If we let [tex]b=x(x+1)[/tex] and [tex]c=x+1[/tex] then we now have:

    [tex]a\left(x(x+1)+(x+1)\right)[/tex] but this time we aren't completely done because b and c have a common factor also. [tex]x(x+1)+(x+1)=x(x+1)+1(x+1)=(x+1)(x+1)=(x+1)^2[/tex]

    So lets put it all together now in [tex]ab+ac=a(b+c)[/tex] where [tex]a=x^2(x+1)^2, b=x(x+1), c=x+1[/tex]

    [tex]x^2(x+1)^2(x(x+1)+(x+1))=x^2(x+1)^2(x+1)^2=x^2(x+1)^4[/tex] This last form is completely factorized.


    Now looking at your expression: let some other variable such as [tex]y=(3x+2)^3[/tex] and see if that makes things easier to factorize. Also you'll need to factorize [tex]2x^2-3x+1[/tex], can you do this?
     
  4. Feb 4, 2010 #3
    well i'll sure try to do it. thank you very much for your time and this lengthy explanation!
     
  5. Feb 4, 2010 #4
    i think i got it! if i'm correct i can factor out a (3x+2)^3 and that makes thing a whole lot simpler
     
  6. Feb 4, 2010 #5

    Mentallic

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    Homework Helper

    No problem! :smile:

    Yep :wink:
     
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