i am terrible at factoring and i would like some much needed help with these!
a) 36(2x - y)^2 - 25(u - 2y)^2
b) x^2 - y^2 + z^2 - 2xz
c) x^2 + 2 + 1/x^2
d) p^2 - 2p + 1 - y^2 - 2yz - z^2
thanks!!!
I can help you with these, anyway:
c) $\displaystyle x^2 + 2 + \frac{1}{x^2}$
If this were $\displaystyle a^2 + 2ab + b^2$ you would have no trouble factoring it (I presume).
Let $\displaystyle a = x$ and $\displaystyle b = \frac{1}{x}$
Then your expression becomes:
$\displaystyle a^2 + 2ab + b^2 = (a + b)^2 = \left ( x + \frac{1}{x} \right ) ^2$
This is a useful little trick to remember. You'll see this kind of factoring every now and again.
d)
$\displaystyle p^2 - 2p + 1 - y^2 - 2yz - z^2$
$\displaystyle (p^2 - 2p + 1) - (y^2 + 2yz + z^2)$
$\displaystyle (p - 1)^2 - (y + z)^2$
Nothing more you can do here.
-Dan
I only get mad at myself. I don't mind making the occasional mistake, because everyone does at some point and because there are skilled workers here who will catch them.
What I get frustrated about is when I keep making mistakes over and over and over... That means I'm simply working too fast and that doesn't really help the people who have asked for it.
(Not to mention I have nearly as god-like an ego as ThePerfectHacker. Don't tell him that, though, because he might feel that there isn't enough Hilbert space here for the two of us! )
-Dan