MHB Expanding and simplifying brackets

AI Thread Summary
The discussion focuses on the steps to simplify and expand the expression involving brackets, specifically the equation $4d^2R^2 - (d^2-r^2+R^2)^2$. The user seeks guidance on obtaining four brackets from this expression, utilizing the difference of squares method. Key transformations include expressing the equation as $(2dR)^2 - (d^2-r^2+R^2)^2$ and factoring it into two products. The process involves multiple steps of factoring and rearranging terms, ultimately leading to a final expression of four distinct factors. The user expresses gratitude for assistance in this mathematical endeavor.
Maggie_s2020
Messages
2
Reaction score
0
Hello, I have been trying to solve the top line equation to get the result (the bottom line). I am searching for a clue (the steps) on how to obtain those four brackets as a result.
Screenshot 2020-12-06 at 16.41.07.png
 
Last edited by a moderator:
Mathematics news on Phys.org
factoring the expression within the radical just involves the difference of squares ...

$4d^2R^2 - (d^2-r^2+R^2)^2$

$(2dR)^2 - (d^2-r^2+R^2)^2$

$[2dR -(d^2-r^2+R^2)] \cdot [2dR + (d^2-r^2+R^2)]$

$[-(d^2-2dR+R^2) + r^2] \cdot [(d^2+2dR+R^2) - r^2]$

$[r^2-(d-R)^2] \cdot [(d+R)^2 - r^2]$

$[(r-d+R)(r+d-R)] \cdot [(d+R-r)(d+R+r)]$

multiply the two middle factors by (-1) ...

$(-d+r+R)(-d-r+R)(-d+r-R)(d+r+R)$
 
Last edited by a moderator:
skeeter said:
factoring the expression within the radical just involves the difference of squares ...

$4d^2R^2 - (d^2-r^2+R^2)$

$(2dR)^2 - (d^2-r^2+R^2)^2$

$[2dR -(d^2-r^2+R^2)] \cdot [2dR + (d^2-r^2+R^2)]$

$[-(d^2-2dR+R^2) + r^2] \cdot [(d^2+2dR+R^2) - r^2]$

$[r^2-(d-R)^2] \cdot [(d+R)^2 - r^2]$

$[(r-d+R)(r+d-R)] \cdot [(d+R-r)(d+R+r)]$

multiply the two middle factors by (-1) ...

$(-d+r+R)(-d-r+R)(-d+r-R)(d+r+R)$
THANK YOU SO SO SO MUCH! BLESS YOU!
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top