How to Expand Algebraic Identities

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Discussion Overview

The discussion centers around the expansion of algebraic identities, specifically focusing on manipulating expressions to match a given form. Participants are exploring methods for expanding both sides of an equation to verify their equivalence.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in expanding the left-hand side to match the right-hand side of an equation.
  • Another participant suggests that multiplying out the brackets on both sides could be a straightforward approach to check for equivalence.
  • A different participant hints that expanding the right-hand side first may reveal cancellations that simplify the process.
  • Additionally, a participant references known algebraic identities, providing specific expansions for expressions like (m + n)² and (w+x)(y+z), and outlines how these can be applied in the context of the problem.

Areas of Agreement / Disagreement

There is no clear consensus on the best method to approach the problem, as participants suggest different strategies and techniques for expansion.

Contextual Notes

Participants have not fully resolved the steps involved in the expansion, and there may be assumptions regarding the familiarity with algebraic identities that are not explicitly stated.

NotaMathPerson
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Hello! Please help me start solving this.

View attachment 5567

I did expand the lhs but I still can't make it to be like the rhs. Any help would be appreciated!
 

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There may be neater ways to do this, but you can't go wrong if you simply multiply out the brackets on both sides and see whether they give the same answer.
 
Hint: expand the right-hand side, first. You'll find some stuff "cancels".
 
According to Opalg, you probably know (m + n)² = m² + 2mn + n².
Also, $$(w+x)(y+z)=wy+xy+wz+xz$$.
Therefore, $$(wy+xy+wz+xz)(\alpha+\beta)=\alpha wy+\alpha xy+\alpha wz+\alpha xz+\beta wy+\beta xy+\beta wz+\beta xz$$.
 

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