# Factorize the following expression

1. Jul 29, 2010

### abrowaqas

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. Jul 29, 2010

### Char. Limit

So, what's the question? I see an expression, told to factorize, and I see the solution. What's your question?

3. Jul 29, 2010

### 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.

4. Jul 29, 2010

### vela

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

\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*}

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

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