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Yet another simple factorizing question

  1. Mar 1, 2008 #1
    [SOLVED] yet another simple factorizing question..

    I wont re-write the full question, just one line on the numerator:

    from the solutions, (a + 1)^2 − (a − 1)^2 factorizes to:

    ((a + 1) − (a − 1))((a + 1) + (a − 1))

    I can see that this is just another form of:

    (a + 1)(a + 1) - (a - 1)(a - 1)

    but why is the former, and not the later used?

    does it make it easier to go to the next step to complete factorization process?

    If so please explain why.
  2. jcsd
  3. Mar 1, 2008 #2


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    Well, it's going to depend on what the question asks next!
  4. Mar 1, 2008 #3
    the solution continues on like this:

    = (a + 1 − a + 1)(a + 1 + a − 1)

    = 4a

    (the question is to factorize.. i dont know what you mean by "what does it ask next")
    Last edited: Mar 1, 2008
  5. Mar 1, 2008 #4


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    Ok, I think I get what you mean now. Well, your first expression is in the form x^2-y^2, which is a difference of two squares. We know that the factorisation of a difference of two squares is (x+y)(x-y); it just turns out that in this case the expression simplifies further.

    The second expression you give in your first post is not a factorisation of (a+1)^2-(a-1)^2, but is an expansion.
  6. Mar 1, 2008 #5
    thank you, understood
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