So, let's say that you have this expression:

(x - a)

and you need to get it under the square root sign. What is the right way to do it?

I came up with two methods, hopefully at least one of them is right. I want to find out which is right and to read more on the topic in order to understand WHY it is right.

First way:

$\displaystyle x - a = \sqrt{x^2 - a^2} = \sqrt{(x-a)(x+a)}$

Mr F says: This is totally wrong. What happens if x = 2 and a = 1, for example? You're meant to learn something from previous questions that you posted: http://www.mathhelpforum.com/math-he...equal-1-a.html
Second way:

$\displaystyle x - a = \sqrt{(x-a)^2} = \sqrt{x^2 - 2xa + a^2}$

Mr F says: This is wrong too. $\displaystyle \sqrt{(x - a)^2} = |x - a|$ not x - a.
I can't find any videos on youtube or texts on the math sites, because I don't know which keywords to use in order to find it - any help would be appreciated.