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Homework Help: Difficult factorisation

  1. Aug 9, 2011 #1
    The problem

    Factorize: [itex] a^{2}-\left ( b+c \right )^{2}[/itex]

    expanded it to see if I can find any solution:

    [itex] \left ( b+c \right )^{2}=b^{2}+2bc+c^{2}[/itex]

    [itex] a^{2}-\left ( b^{2}+2bc+c^{2} \right ) [/itex]

    [itex] a^{2}- b^{2}-2bc-c^{2} \right )[/itex]

    But I can’t get any further.
    What should I do now to simplify it? Please explain and show me a couple of clues or something?
  2. jcsd
  3. Aug 9, 2011 #2
    Hello there.

    What do you know about the factorization of a difference of squares?
  4. Aug 9, 2011 #3
    Ok so the solution could easily be found by just applying the distributive law?

    I'm gonna try.
  5. Aug 9, 2011 #4


    Staff: Mentor

    More specifically, use the fact that a2 - b2 = (a + b)(a - b). That's what stringy was getting at.
  6. Aug 9, 2011 #5
    EDIT: Mark44 beat me to it. For future reference, the difference of squares refers to the identity that Mark44 wrote.
  7. Aug 9, 2011 #6
    Thank you. I will return later with my answer.
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