How do you factor #x^2 - 2c - c^2#?

1 Answer
Mr. Mike
Mar 29, 2018

#x^2-c(2+c)=[x+sqrt(c(2+c))][x-sqrt(c(2+c))]#

Explanation:

We want to factor #x^2-2c-c^2#.

First, let's factor #-c# from the last two terms.

#x^2-c(2+c)#

Now picture this expression as the difference of two squares. Don't see it? Well, obviously #x^2# is the square of #x#. But what expression, when squared would give #c(2+c)#? That would be #sqrt(c(2+c))# of course!

We know that for the difference of two squares #a^2-b^2=(a+b)(a-b)# so in this case,

#x^2-c(2+c)=[x+sqrt(c(2+c))][x-sqrt(c(2+c))]#.

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