Factoring Problem a^2 - b^2 + 2bc - c^2

[A_Moose]

[SOLVED] Factoring problem

Homework Statement
Factorize the following: a^2 - b^2 + 2bc - c^2

The attempt at a solution
I know this should be a fairly simple problem, but my brain must be fried or something, I can't seem to come up with anything... There are no factors common to all terms, and I can't spot anything I can do to this thing... I know, it's going to turn out to be me missing something really simple, but I've been staring at this for a while now.

 

[antonantal]

Does this help:

a^2 - b^2 + 2bc - c^2 = a^2 - (b^2 - 2bc + c^2)

?

 

[A_Moose]

Wow, now I feel like a moron.
Thanks for the help, lol.
So, a^2-(b-c)(b-c)... Is that as far as it'll go, or am I missing something again?

 

[antonantal]

Factoring is the decomposition of a polynomial into a product of other polynomials. This means that the final form of that expression should be a product of 2 or 3 or more parenthesis.

How do you factorize x^2 - y^2 ?
See if that applies to your expression.

 

[A_Moose]

Grrr, I'm certainly getting in my "stupid stuff" quota for the day...

(a+(b-c))(a-(b-c))?

 

[antonantal]

Correct!
It's not about smartness. It's just about practice.

 

[A_Moose]

Well, thanks a lot for the help. You, sir, are a life-saver.