# Thread: having problems factoring these 2 equations

1. ## having problems factoring these 2 equations

y= x^3 - x^2
y=(x-2)^3 - (x-2)^2

these are 2 functions for which i am trying to find the roots

2. Originally Posted by tappinniamke
y= x^3 - x^2
y=(x-2)^3 - (x-2)^2

these are 2 functions for which i am trying to find the roots
$\displaystyle y = {x^3} - {x^2} = (x^2)(x-1)$

$\displaystyle y = (x-2)^{3} - {(x-2)^{2}}= {(x-2)^{2}}((x-2)-1)= (x-2)(x-2)(x-3)$

3. thanks i made it alot more complicated in my head than it needed to be

4. just with the second question...
(x-2)^3 - (x-2)^2

sometimes it helps to give the common factor, in this case (x-2) a letter say for example z. this just makes factorizing a little easier.

for example:

let (x-2) = z
so the new equation (if we sub in z whenever we see a (x-2) becomes:
z^3 - z^2
so this factorized becomes
z^2(z-1)
and now sub in for z (x-2)
(x-2)^2((x-2)-1)
which is equal to:
(x-2)^2(x-3)

hope that helps a little for in the future!