Trouble understanding why two equations give the same result

  • Context: High School 
  • Thread starter Thread starter Sam Scott
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Discussion Overview

The discussion revolves around understanding the equivalence of two mathematical expressions: a^2 - (b^2a^2 / c^2) and a^2(1 - (b^2 / c^2)). Participants seek clarification on how these expressions relate to each other, focusing on concepts such as the distributive law and factoring. The scope includes conceptual clarification and mathematical reasoning.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the equivalence of the two equations and seeks guidance on what to study to understand it better.
  • Another participant suggests reviewing the "distributive law" as a potential key to understanding the relationship between the equations.
  • A participant questions the meaning of specific terms in the equations, prompting further exploration of the expressions involved.
  • One participant proposes that if b^2/c^2 is denoted as x, it becomes clearer that a^2 - a^2x is equivalent to a^2(1 - x), emphasizing the role of common factors in expressions.
  • Another participant acknowledges their initial confusion and expresses gratitude for the assistance received, indicating a learning process.
  • A participant clarifies the multiplication of terms in the context of the equations, reinforcing the understanding of the expressions.

Areas of Agreement / Disagreement

Participants appear to share a common understanding of the mathematical concepts being discussed, but there is no explicit consensus on the initial confusion experienced by the original poster. The discussion remains focused on clarification rather than resolving the initial uncertainty.

Contextual Notes

Some participants express uncertainty about applying the distributive law to the equations, indicating a need for further exploration of foundational concepts. The discussion does not resolve the initial confusion but rather facilitates a deeper understanding of the mathematical relationships involved.

Sam Scott
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Hello,

I feel like I should know this already and feel foolish having to ask, however can someone please explain why:

[tex]a^2 - \frac {b^2a^2} {c^2} = d[/tex] is the same as: [tex]a^2 (1 - \frac {b^2} {c^2}) = d[/tex]

Again, sorry if this really is something incredibly obvious, for some reason I am just blanking. All I need to know is what I need to look up to understand

Thank you in advance and this is my first post so I am sorry if this is in the wrong area or anything like that,

Sam
 
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Reread what you've been taught/learned about the "distributive law."
 
Thank you for replying, I'm re-reading what I have on the distributive law but I can't see how to apply that to the equation, I'm sorry about this, I've been looking around for a long time by myself not wanting to waste anybody's time and now when somebody is telling me what to look at I'm still not seeing it.
 
What's "a2 x 1 ?" What's "a2 x b2/c2 ?"
 
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So in summary yes I was being an idiot. Truly have no idea why this has caused me a problem, but thank you very much for your help!

Very glad I've found this site as something like this is bound to happen to me at some point (for example in the next hour maybe?)

Sam
 
If we call b2/c2 x, would it be obvious that a2 - a2x is the same as a2(1 - x) ?.

In general when sonething appears in every term of an expression it is a factor of that expression.
 
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That also helps, thank you as well! Hopefully I've replied quickly enough to stay out of your black book
 
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Since this isn't really a homework problem (that I can see), I have moved it.
 
Keep in mind that

[tex]a^2\times \frac{b^2}{c^2}=a^2\frac{b^2}{c^2}=\frac{a^2b^2}{c^2}=\frac{b^2a^2}{c^2}[/tex]
 

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