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

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Homework Help Overview

The discussion revolves around the factoring of the expression a^2 - b^2 + 2bc - c^2, which falls under the subject area of algebra, specifically polynomial factoring.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore different ways to rearrange and factor the expression, with one participant attempting to rewrite it in a different form and others questioning the completeness of their factoring attempts.

Discussion Status

The discussion is active, with participants providing insights and suggestions on how to approach the factoring problem. Some have offered partial factorizations while others reflect on their understanding of the concepts involved.

Contextual Notes

There is a sense of frustration among participants regarding the simplicity of the problem, indicating that they may be grappling with confidence in their algebra skills. The original poster expresses difficulty in identifying common factors and recognizing the structure of the expression.

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[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.
 
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Does this help:

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

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

(a+(b-c))(a-(b-c))?
 
Correct!
It's not about smartness. It's just about practice.
 
Well, thanks a lot for the help. You, sir, are a life-saver.
 

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