Question

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

Answer 1

`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))]`.