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(a+b)^2 using mulitplying in brackets

  1. Feb 2, 2012 #1
    question im working on at the moment is squares


    when is (a+b)^2 eather (a+b)(a+b) useing foils law or when (a+b)(a-b) using foils law.
    im stuck to when you use which one.



    i think they are when you use quadratic x^2+x+1=0 for the first one or -1 at the end for the second one.
    i hope you can help.




    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 2, 2012 #2

    eumyang

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    Homework Helper

    When you square a number, you multiply that number by itself. So
    (a + b)2 = (a + b)(a + b). Also,
    (a - b)2 = (a - b)(a - b).

    Well, you won't be able to use any of the special product patterns with either of the quadratics above.
    (a + b)2 = a2 + 2ab + b2, and
    (a - b)2 = a2 - 2ab + b2, and
    they don't fit in either quadratic above.
     
  4. Feb 2, 2012 #3
    thank you,it would only be just with a quadratic and factoring you have + and a - would this be using the which (a+b)^2 or is this some thing else.
     
  5. Feb 2, 2012 #4

    eumyang

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    For example, if you had a quadratic
    4x2 + 20x + 25 = 0,
    you can use the special product
    (a + b)2 = a2 + 2ab + b2
    because
    4x2 + 20x + 25 = (2x)2 + 2(2x)(5) + 52,
    and this follows the pattern
    a2 + 2ab + b2.

    So
    4x2 + 20x + 25 = 0
    (2x)2 + 2(2x)(5) + 52 = 0
    (2x + 5)2 = 0
    ... and so on.

    Another example: for this quadratic,
    x2 - 14x + 49 = 0,
    you can use the special product
    (a - b)2 = a2 - 2ab + b2
    because
    x2 - 14x + 49 = x2 - 2(x)(7) + 72,
    which follows the pattern
    a2 - 2ab + b2.

    So
    x2 - 14x + 49 = 0
    x2 - 2(x)(7) + 72 = 0
    (x - 7)2 = 0.
    ... etc.

    You mentioned the sum and difference pattern, which is
    (a + b)(a - b) = a2 - b2.

    You can use this pattern in a quadratic like this one:
    25x2 - 64 = 0,
    like this:
    25x2 - 64 = 0
    (5x)2 - 82 = 0
    (5x + 8)(5x - 8) = 0
    ... etc.

    This is an example of a quadratic that would not fit any of the three patterns above:
    x2 + 12x - 64 = 0
    However, it can be factored into
    x2 + 12x - 64 = 0
    (x + 16)(x - 4) = 0
    ... and can be solved by using the zero product property.
     
  6. Feb 2, 2012 #5
    Thank you ,this is helpfull.Have a good day.may your pc never lag :)
     
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