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Homework Help: Factorize the following expression

  1. Jul 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Expression is
    p^3-(x^2+xy+y^2)p+xy^2+x^2y=0 where ^ shows power

    2. Relevant equations


    3. The attempt at a solution
    the solution is
    (p-x)(p-y)(p+x+y)=0
     
  2. jcsd
  3. Jul 29, 2010 #2

    Char. Limit

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    Gold Member

    So, what's the question? I see an expression, told to factorize, and I see the solution. What's your question?
     
  4. Jul 29, 2010 #3

    Mark44

    Staff: Mentor

    The OP would like to factor the expression on the left side of the equation, and is showing the solution shown in the book, but doesn't know how to get the factorization that is shown.

    I believe the best way to crack this one is to use a known formula for factoring a cubic. Here's a discussion of several techniques - http://en.wikipedia.org/wiki/Cubic_equation. See the section titled "Cardano's method" on the linked-to page.

    Factoring cubic equations is a lot more complicated than factoring quadratics, but the saving grace here is that there is no quadratic (p2) term in your equation, which should make the work a little easier.
     
  5. Jul 29, 2010 #4

    vela

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Try adding and subtracting pxy to what's inside the parentheses to get

    [tex]\begin{align*}
    0 &= p^3-(x^2+xy+y^2+xy-xy)p+xy^2+x^2y \\
    &=p^3-(x^2+2xy+y^2)p + pxy + xy^2+x^2y \\
    &=p^3-(x+y)^2p+pxy+xy^2+x^2y
    \end{align*}
    [/tex]

    Then pull common factors out of the first two terms and the last two terms. That should get you started.
     
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