# Factorization question

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• April 27th 2013, 10:39 PM
anneshirleygilbert
Factorization question
Can somebody please help me with this factorization question:

Factorise fully 3x3y - 3x2y + 6xy - y + (xy)/2 - (x2y)/2

I tried this question and this is what I have done:

= 3xy (x2 - x + 2) - y (1 + x/2 -x2/2)

Can't go beyond this .... please help. TIA
• April 27th 2013, 10:48 PM
Prove It
Re: Factorization question
Quote:

Originally Posted by anneshirleygilbert
Can somebody please help me with this factorization question:

Factorise fully 3x3y - 3x2y + 6xy - y + (xy)/2 - (x2y)/2

I tried this question and this is what I have done:

= 3xy (x2 - x + 2) - y (1 + x/2 -x2/2)

Can't go beyond this .... please help. TIA

You've made a good start, although you have a sign error. It should be

\displaystyle \begin{align*} 3\,x^3y - 3\,x^2y + 6\,x\,y - y + \frac{x\,y}{2} - \frac{x^2y}{2} &= 3\,x\,y \left( x^2 - x + 2 \right) - y \left( 1 - \frac{x}{2} + \frac{x^2}{2} \right) \\ &= 3\, x\, y \left( x^2 - x + 2 \right) - \frac{y}{2} \left( x^2 - x + 2 \right) \\ &= \left( x^2 - x + 2 \right) \left( 3\,x\,y - \frac{y}{2} \right) \end{align*}
• April 28th 2013, 12:14 AM
anneshirleygilbert
Re: Factorization question
Thanks so much, Prove It! Really appreciate your help! Have a good day... or is it night?
• April 28th 2013, 12:27 AM
Prove It
Re: Factorization question
Night now :)