# Factorization question

• April 27th 2013, 11:39 PM
anneshirleygilbert
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)

• April 27th 2013, 11:48 PM
Prove It
Re: Factorization question
Quote:

Originally Posted by anneshirleygilbert

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)

\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*}