Algebra Question(Part of a Larger Problem)

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Homework Help Overview

The discussion revolves around simplifying the algebraic expression f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2). Participants are seeking clarity on the simplification process and how to arrive at the provided answer in the textbook.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss factoring out common terms from the expression and question the accuracy of their intermediate steps in the simplification process.

Discussion Status

Some participants have offered guidance on factoring out common elements, while others are verifying their calculations and addressing mistakes. The discussion reflects a collaborative effort to clarify the simplification process without reaching a definitive conclusion.

Contextual Notes

There is an indication that the original poster is struggling with the simplification despite it being described as an easy task. The presence of a textbook answer suggests a standard approach that may not have been fully grasped by the original poster.

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Homework Statement


f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2)

Need to simplify.


Homework Equations





The Attempt at a Solution


I tried simplifying completely but my answer wasn't even close. The Back of the book has:
5x(x-5)^(2)(x-2)

I know its easy, but I'm drawing a blank...can anyone start me off on the right path to find how they got that answer?
 
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The first thing to notice is that both terms in your expression have a common factor of x*(x-5)^2. Factor that out. Now what's left in each term?
 
Well, wouldn't it then be 2(x-5) + (3x+1)?
 
I get just 2(x-5)+3x. Where did the 1 come from?
 
Oh! I got it!

Oh wow. I can't believe I had made a mistake like that. Thank you so much. I just figured it out.

Thanks Dick.
 

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