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Homework Help: Removing parantheses

  1. May 22, 2008 #1
    Silly question but this kind of threw me:

    a + 2b - (-a + b) =

    So, when you remove the parantheses, you change the sign. So I figured it would go like this:

    a + 2b - a - b = b

    (by this logic: - (-a + b) = - +a -b = -a -b)

    But my books says

    a + 2b + a - b = 2a + b

    I'm guessing the book is right, but where am I stepping wrong?

  2. jcsd
  3. May 22, 2008 #2


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    Staff Emeritus
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    You are basically looking to expand [itex]-1\cdot(-a+b)=(-1)(-a)+(-1)(b)[/itex]

    Can you simplify this?
  4. May 22, 2008 #3
    I thought I did, but it seems I dont :/

    (-1)(-a) + (-1)(b) = a + (-b) = a + b

  5. May 22, 2008 #4
    You got real close. You correctly figured that (-1)(-a) amounts to the 'a'
    So look close at (-1)(b), and note that you think it amounts to 'b', which is wrong!
    is what you were thinking

    (-1)(-a) + (-1)(b) = a + (-b) = a - b is what I am thinking.

    OK - so you now know that a minus sign in front of anything, (even stuff in brackets) is like saying it is multiplied by -1. Now move on and get it all quicker like this... start again... Take it from the left.
    a + 2b - (-a + b)

    There's a+2b which we leave alone for now. Work on the -(-a+b)

    Think "two minusus multiplied out make a plus" so the first term will be 'a'
    Now make the minus sign outside the work on the next term inside.
    Ahh, its a minus times a plus, which makes a minus. That results in -b
    Put them together. You get a - b

    Now finally bring back the a + 2b, and you get a + 2b + a - b

    I leave it to you to finally push the a's and b's together, and come up with the final simplest expression.
  6. May 23, 2008 #5
    (-1)(-a) + (-1)(b) = a + (-b) = a + b

    Ugh, that was a nasty little typo, it is supposed to read = a - b.

    Thanks for the responses, I appreciate it.

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