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Homework Help: Quick Factoring Help

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Could someone help me factor,
    ((x-1)y^2)+(1-(x^2))





    3. The attempt at a solution
    Is it possible to get to:
    (x-1)(y^2-x-1)?
     
  2. jcsd
  3. Sep 28, 2010 #2

    fss

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    Yes, it is possible to get there.

    Work with the left-hand term; 1-x2. When you factor that, things should start looking more manageable.
     
  4. Sep 28, 2010 #3
    So I get (x-1)y^2 + (1-x)(1-x)

    Where do I go from there in order to factor out the (x-1)?
     
  5. Sep 28, 2010 #4

    fss

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    What happens if you take out a -1 from one of the terms on the right?
     
  6. Sep 28, 2010 #5
    Oh so, I got (x-1)y^2 - (x+1)(x-1) COrrect?
     
    Last edited: Sep 28, 2010
  7. Sep 28, 2010 #6

    fss

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    You can take out -1 from just the right-hand term.

    (x-1)y^2 + (1-x)(1-x) = (x-1)y^2 + (-1) (?????) (1-x)
     
  8. Sep 28, 2010 #7
    Ok, so I got: (x-1)y^2 - (x+1)(x-1)
     
  9. Sep 28, 2010 #8

    fss

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    Incorrect. Look at the bolded term again. You're only taking -1 out of one quantity in the parentheses.
     
  10. Sep 28, 2010 #9
    Oh, so would it be:
    (x-1)y^2 - (-x-1)(x-1)?

    But how do I get to:
    (x-1)(y^2-x-1)?
     
  11. Sep 28, 2010 #10

    fss

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    Oops, sorry, in post #3 you made an error which I didn't notice initially.

    You need to factor this correctly for it to make any sense. Once you have it factored correctly and you take out a (-1) from one of the terms in the parentheses, you should be able to then rearrange the expression into something that resembles what you're trying to show.

    Hint: you already know how the result needs to look. Use this to your advantage...
     
  12. Sep 29, 2010 #11

    Mentallic

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    Homework Helper

    All you really need are these 3 rules:

    [tex]a^2-b^2=(a-b)(a+b)[/tex]

    [tex]ab=-(-a)(b)=-(a)(-b)[/tex]

    [tex]ab+ac=a(b+c)[/tex]

    Notice the first difference of two squares, as fss has pointed out you have made a mistake in factoring the 1-x2, so fix that first before moving on.
     
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