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!!!

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- Sep 5th 2007, 03:18 PMcheckmarksfactoring hmwk...please help?
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!!! - Sep 5th 2007, 03:36 PMtopsquark
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 - Sep 5th 2007, 04:18 PMKrizalid
- Sep 5th 2007, 05:25 PMcheckmarks
- Sep 5th 2007, 05:31 PMKrizalid
- Sep 5th 2007, 05:39 PMtopsquark
- Sep 5th 2007, 05:45 PMKrizalid
I hope you don't get mad.

There're just details, it's nothing to worry about :) - Sep 5th 2007, 06:15 PMtopsquark
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