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Factoring Polynomials

  1. Feb 20, 2006 #1
    I am stuck on this one polynomail factoring problem and I was wondering if someone could help me with it:

    16a^2 - 24ab + 9b^2 - 25c^2

    I tried factoring the first 3 terms as a trinomial but I'm not sure if that's what I'm supposed to do. What I wrote down so far is:

    (4a -5c)(4a +5c)
  2. jcsd
  3. Feb 20, 2006 #2
    Note: There should be a space between the 5c and 4a
  4. Feb 20, 2006 #3


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    Hint: Express the first three terms as a perfect square then factor the difference between squares. :)
  5. Feb 20, 2006 #4
    [tex] (16a^2-24ab+9b^2)-25c^2 [/tex]
    [tex] (4a-3b)^2-25c^2 [/tex]

    Now note that this is in the form of the difference of two squares, i.e.
    [tex] x^2-y^2 = (x+y)(x-y) [/tex] where x = 4a-3b and y = 5c. So finally:
    [tex] (16a^2-24ab+9b^2)-25c^2 = (4a-3b+5c)(4a-3b-5c) [/tex].

    (And, of course, always multiply it back out to check the answer.)

  6. Feb 21, 2006 #5
    and of course, after you find X, put it into the original problem to make sure your value works.
  7. Feb 21, 2006 #6


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    I think you should leave something for the OP to do! :)
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