MHB How to Expand Algebraic Identities

  • Thread starter Thread starter NotaMathPerson
  • Start date Start date
  • Tags Tags
    Identity
Click For Summary
To expand algebraic identities effectively, start by multiplying out the brackets on both sides of the equation to check for equivalence. It's recommended to first expand the right-hand side, as this can reveal cancellations that simplify the process. The identity (m + n)² = m² + 2mn + n² is a useful reference for expansion. Additionally, the expansion of the product (w+x)(y+z) can be applied to further simplify the expression. Following these steps should help in achieving the desired form of the equation.
NotaMathPerson
Messages
82
Reaction score
0
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!
 

Attachments

  • ALGEBRA.jpg
    ALGEBRA.jpg
    12.2 KB · Views: 109
Last edited:
Mathematics news on Phys.org
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, $$(wy+xy+wz+xz)(\alpha+\beta)=\alpha wy+\alpha xy+\alpha wz+\alpha xz+\beta wy+\beta xy+\beta wz+\beta xz$$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Am I misapplying something here? (Exponentials; Euler's identity)
  • · Replies 3 ·
Replies
3
Views
549
Undergrad Why did I lose 60% on my proof of Generalized Vandermonde's Identity?
  • · Replies 3 ·
Replies
3
Views
1K
MHB Solve Situational Problems Involving Trigonometric Identities
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Variant of Baker-Campbell-Hausdorff Formula
  • · Replies 3 ·
Replies
3
Views
2K
MHB Expanding Brackets: Math Help for 2nd Term Maths
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Practice With Proofs? (Algebra, Trig, and Calc)
  • · Replies 6 ·
Replies
6
Views
2K
High School Why Does This Algebraic Identity Work in Relativistic Doppler Calculations?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Which of the following are equal to this identity?
  • · Replies 4 ·
Replies
4
Views
4K
Proving an Identity: Is my High School Explanation Correct?
  • · Replies 8 ·
Replies
8
Views
3K
Is This Factorial Identity True and How Can It Be Proven?
  • · Replies 5 ·
Replies
5
Views
2K