# Thread: Factorization question

1. ## 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

2. ## Re: Factorization question

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 \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*}

3. ## Re: Factorization question

Thanks so much, Prove It! Really appreciate your help! Have a good day... or is it night?

Night now