MHB Please help for binomial expansion (2x-1/(2x^2))^9

  • Thread starter Thread starter blackholeftw
  • Start date Start date
  • Tags Tags
    Binomial Expansion
AI Thread Summary
The discussion focuses on solving the binomial expansion of the expression (2x - 1/(2x^2))^9. The formula for the general term T_{r+1} is provided, which involves binomial coefficients and powers of the variables. The term is expressed as T_{r+1} = (9!/(r+1)!(8-r)!) * (-1)^{r+1} * 2^{7-2r} * x^{6-3r}. A key point is the relationship established between r and h, leading to the equation 3r - h = 9. The discussion seeks assistance in further simplifying or solving this binomial expansion problem.
blackholeftw
Messages
1
Reaction score
0
As titled, been cracking my head over it.
Thanks in advance!

View attachment 9276
 

Attachments

  • be.png
    be.png
    52.6 KB · Views: 127
Mathematics news on Phys.org
Here’s the first part of the question to get you going ...

For $(a-b)^9$, $\displaystyle T_{r+1} = \binom{9}{r+1} a^{9-(r+1)}(-b)^{r+1}$

$T_{r+1} = \dfrac{9!}{(r+1)!(8-r)!} (2x)^{8-r} \left(-\dfrac{1}{2x^2}\right)^{r+1} = \dfrac{9!}{(r+1)!(8-r)!} (-1)^{r+1} \cdot 2^{7-2r}x^{6-3r}$

Multiplying this term by $x^h$ would yield the variable factor as $x^{6-3r+h} = x^{-3} \implies 3r-h=9$
 
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...

Similar threads

Replies
19
Views
1K
Replies
1
Views
2K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
6
Views
1K
Replies
2
Views
1K
Replies
3
Views
2K
Replies
18
Views
2K
Back
Top