9+10ab-a^2-25b^2

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- May 30th 2007, 12:01 AMCorneliusPlease help to solve
9+10ab-a^2-25b^2

- May 30th 2007, 02:12 AMjanvdl
- May 30th 2007, 03:57 AMCaptainBlack
- May 30th 2007, 06:40 AMtopsquark
Are you supposed to factor this?

$\displaystyle 9 + (-a^2 + 10ab - 25b^2)$

$\displaystyle = 9 - (a^2 -10ab + 25b^2)$

$\displaystyle = 9 - (a - 5b)^2$

$\displaystyle = 3^2 - (a - 5b)^2$ <-- This is the difference of two perfect squares

$\displaystyle = [ 3 + (a - 5b) ] [ 3 - (a - 5b) ] $

$\displaystyle = (3 + a - 5b)(3 - a + 5b)$

-Dan