What is the Expanded Formula for a Square?

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Discussion Overview

The discussion revolves around the expansion of a mathematical expression involving differences of variables, specifically examining whether the book's expansion is correct. The scope includes mathematical reasoning and clarification of algebraic identities.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the book's expansion of the expression \([(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)]\) to \((x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2\), suggesting there may be a mistake.
  • Another participant agrees that the two expressions are not equal, clarifying that \([(x3-x2)+(x2-x1)]*[(x3-x2)+(x2-x1)]\) correctly expands to \((x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2\).
  • A third participant points out a potential typographical error in the original expressions, noting a change from "+" to "-" in one of the brackets.
  • One participant acknowledges the typographical error, suggesting it was a mistake.
  • Another participant relates the expression to the standard formula for a square, indicating that with the negative sign, it aligns with the identity \((a+b)*(a+b)= a^2+ 2ab+ b^2\), where \(a= x3-x2\) and \(b= x2- x1\).

Areas of Agreement / Disagreement

Participants generally agree that there is a mistake in the book's expansion due to a typographical error. However, there is no consensus on the correctness of the original expression as presented in the book.

Contextual Notes

The discussion highlights the importance of careful attention to signs in algebraic expressions, as well as the potential for typographical errors to lead to confusion in mathematical reasoning.

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[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)]
the book expands it to:
(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

i didnt get it so can someone please help me in this, i think there is a mistake in the book.
 
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Originally posted by loop quantum gravity
[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)]
the book expands it to:
(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2
[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)] does not equal to(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

However,
[(x3-x2)+(x2-x1)]*[(x3-x2)+(x2-x1)] = (x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2
 


Originally posted by KL Kam
[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)] does not equal to(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

However,
[(x3-x2)+(x2-x1)]*[(x3-x2)+(x2-x1)] = (x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2
have you noticed the experssions on the right are the same?
 
Last edited:
Please read the expressions on the left hand sides carefully. I changed a "+" sign to a "-" sign in the third small bracket
 
yes you are right. i guess it was a type mistake )-:
 
With the negative, it is simply the formula for a square:

(a+b)*(a+b)= a2+ 2ab+ b2

with a= x3-x2 and b= x2- x1
 

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