Factoring 28s^2 + 8st - 20t^2: A Simplified Explanation and Solution

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Homework Help Overview

The problem involves factoring the quadratic expression 28s^2 + 8st - 20t^2. The original poster references a solution found in a textbook and expresses confusion regarding their own attempts at factoring the expression.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss various attempts at rearranging and combining terms to simplify the expression for factoring. Questions are raised about potential tricks or methods that might clarify the factoring process.

Discussion Status

Some participants have offered suggestions for combining terms and rethinking the expression, indicating a collaborative effort to explore different approaches. The original poster expresses a realization about their misunderstanding, suggesting progress in their understanding of the problem.

Contextual Notes

The original poster expresses frustration with the presence of the t^2 term, indicating it may have contributed to their confusion. There is no indication of any imposed homework rules or constraints mentioned in the discussion.

Rowah
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Homework Statement



[tex]28s^2 + 8st - 20t^2[/tex]

The answer in the back of the book is 4(7s - 5t)(s + t)

2. The attempt at a solution

[tex]4(7s^2 + st + st - 5t^2)[/tex]
[tex]4(7s^2 + st + st - 20t^2)[/tex]
[tex]4(s(7s + t) + t(s - 20t))[/tex]

I'm lost, can someone please help me?

Thanks in advance.
 
Last edited:
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In your first attempt at the solution, why not combine the second and third terms inside the (), it might make things more obvious.
 
Is there some trick to this that I am missing?

[tex]4(7s^2 + 2st - 5t^2)[/tex]
 
Well, you could note that 2st=7st-5st, which makes your expression 4(7s2+7st-5st-5t2). Is this any easier to factorise?
 
OHH OHH OHHHH OHHHHHH!

Oh my god, how could I be so blind? That t^2 at the end threw me off. I feel like such an idiot. Thanks a billion cristo and robb, and I apologize for wasting your time :)
 

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