# Thread: Simplify (6a^2 + a - 2)(2a^2 - 3a + 1)

1. ## Simplify (6a^2 + a - 2)(2a^2 - 3a + 1)

hey im having trouble with this. pleas help me figure out how to do this problem. i have a test tomorrow and really need this help...im sorry im a noob.

2. Factor the top and bottom: $\displaystyle \displaystyle (3a\pm x )(2a\pm y ) = 6a^2 + a - 2 \ \ni x,y\in\mathbb{Z}$ and do the same for the denominator

3. Originally Posted by greenzspy
hey im having trouble with this. pleas help me figure out how to do this problem. i have a test tomorrow and really need this help...im sorry im a noob.
you need to factor the numerator and denominator and divide out the common factor ...

4. Recognise that

$\displaystyle 6a^2+a-2 = (3a+2)(2a-1)$ and
$\displaystyle 2a^2-3a+1 = (2a-1)(a-1)$.

Putting these together, we obtain

$\displaystyle \frac{6a^2 + a - 2}{(2a^2 - 3a + 1} = \frac{(3a+2)(2a-1)}{(2a-1)(a-1)}=\frac{3a+2}{a-1}$,

where the last step is done under the assumption that

$\displaystyle a\ne\frac{1}{2}_{.}$

If we do not have this assumption, we cannot do the cancellation.