binomial no calc

[lacoste]

how to do this by hand with no calc.( i dont know how to use pascals triangle fully, so could you please explain if you use it)


binomial expansion.

(2/x+3x)^5


thanks

[TrueTears]

do you mean ? lol

[lacoste]

oh sorry truetears, the second one; where 2 is over x by itself only

[TrueTears]

Alright nps

Consider this:

let



Now consider y as having the 'x' and z is just a constant, because the expression in the brackets must have a linear expression to do binomial theorem.

use the binomial theorem on that yields...





Now sub in the values for y and z and there's your answer

[dekoyl]

1
11
121
1331
14641
1,5,10,5,1



I haven't done this in a looong time Hope you understand. Is this right?

[TrueTears]

yeah and dekoyl's way is also correct, he let z as having the 'x' and y as the constant.

[lacoste]

oh yes thanks.

and

find the coefficient of x^2 in the above q


This is such a difficulty

[lacoste]

without part a which was expanding it all

[TrueTears]

There are no coefficients with o.o?

[lacoste]

There are no coefficients with o.o?

Yes, the ans is 0 but how do i know that its 0 without expanding it all out??

[dekoyl]

There are no coefficients with o.o?

Yes, the ans its 0 but how do i know that theres none with expanding it all out??

Just do a quick observation. No need to expand it out. You just have to cancel a few indicies in your head.

[lacoste]

sorry dekoyl but how do i do that?

where?

im not very good

[TrueTears]

You would do this again

let and

now

so, term means the 4th term from the highest right? (ie, )

so lets consider y as containing the 'x' and z as the constant

(remember the term that contains the 'x' always has the power of what you are looking for, so the power of 2 would mean , the power of 3 would mean etc etc)

the fourth term would be which does not contain a

now lets consider z as containing the 'x' and y as the constant

the fourth term would be again this does not contain a

Therefore coefficient of

Hope this helps.

EDIT: dekoyl is just too godly

[dekoyl]

sorry dekoyl but how do i do that?

where?

im not very good

It's okay.

Well the whole thing is to the power of 5. So looking at the two "parts" inside the brackets () you will see that the closest will either be (note k = a constant) or so it's 3 then 1. There is no .

Bah I suck at explaining Hope you understand.


Edit: Wow TrueTears is a beast at typing and latex.

[lacoste]

thankyou everyone!!!!!!

truetears and dekoyl!!!

still dont understand the 'k' part of dekoyl's.
lol


q. what is the coefficient of x^3 in same question above? (what is the terms)