jpknegtel 3 years ago Need to use the binomal therom to expand (1+2x)/(1-2x) Not sure where to start to get it into the right format.

1. jpknegtel

$(1+2x)/(1-2x)$

2. jpknegtel

Oh. Need to go up too and including the term $x ^{2}$

3. King

so its x^2+2x+1/1-2x?

4. jpknegtel

Could you explain the steps? thank you very much for your timee!

5. Zed

Is that $(1+2x) \times (1-2x)$ or $\frac{(1+2x)}{(1-2x)}$?

6. jpknegtel

I have been trying to do those Fractions but am unable to do it! Soo fustrating! Yes it is the the (1+2x) over (1-2x)

7. Zed

Okay give me a minute to work this out :)

8. jpknegtel

If it is any help the answer is $(1+2x)(1+2x+4x ^{2})$

9. y2o2

(1+2x) over (1-2x) can never be equal to (1+2x)(1+2x+4x²) and you can assure that by substitution.

10. Zed

$(1+2x)(1-2x)^{-1}=(1+2x)(1^{-1}+-1*1^{-1-1}*-2x+\frac{-1(-1-1)}{2} (1)^{-1-2}(2x)^2+...)$$=(1+2x)(1^{-1}+2x+\frac{-1(-2)}{2} (1)^{-3}*4x^2+...)$$=(1+2x)(1+2x+\frac{2}{2} *1*4x^2+...)$$=(1+2x)(1+2x+4x^2+...)$ This is from this rule $(a+b)^n=a^n+na^{n-1}b+\frac{n(n-1)}{2}a^{n-2}b^2+....$ Sorry it took so long :D

11. dumbcow

either the answer is wrong or you forgot something when posting the problem i agree with y2o2

12. Zed
13. dumbcow

@zed yes it becomes an infinite sum..is that the solution they are looking for? their answer stops after 4x^2

14. Zed

Yes they only had to do the terms until it reaches x^2 power

15. dumbcow

ok thanks for clearing it up :)

16. jpknegtel

Thank you very much guys! Clears things up!