Question

Can anyone teach me how to do binomial expansion? The sigma thing confused me even more! And, is there an easier way to do it?

Answer 1

\( \color{Black}{\Rightarrow \Large (a + b)^n = \sum_{k = 0}^{n} \binom{n}{k} a^{n - k} b^k }\)

I see. So we have to sum em up right?

Answer 2

Yap!

Answer 3

Let's try it with (a + b)^2

Answer 4

okay, let me give you an easy example question to solve:
(1+x)^3

Answer 5

yeah, try that as well.

Answer 6

\( \color{Black}{\Rightarrow \Large (a + b)^2 = \binom{2}{0}a^{2}\times 1 + ..... }\)

I wrote 1 in this because I b^0 = 1

Answer 7

actually take care of this that for a binomial raised to the nth power, there will be (n+1) terms.

like (a+b)^2 has '3' terms, and so on...

Also, there is something called "Pascal's Triangle". Check this out : http://en.wikipedia.org/wiki/Pascal's_triangle

Answer 8

yeah, complete that^ Parth. That will give you a better insight.

Answer 9

Yeah, I know Pascal's, and I have used it in probability.

Answer 10

Oh I see....will try it on paper lol \(L_AT_EX\) makes it very tedious :P

Answer 11

Thank you @apoorvk :D

Answer 12

Can you tell me about the pascal thing or link me to it?

Answer 13

Hey, can I use a calculator for this? Do people normally use a calculator or what? @apoorvk

Answer 14

No, this is not about a calculator at all - in fact a calculator is generally useless in this thing, unless when you need to find out factorials of large nos.

Answer 15

But this becomes very very very very very very very very tedious :/

Answer 16

I posted a wikipedia link for Pascal's triangle. Try to go through the first part of it, and clear your doubts if any.


No the factorial thing isn't always so long...

like if you have 19!/17!, then if notice, after expanding the factorial, I am only left with a '19x18' in the numerator.

Answer 17

*if ^you

Answer 18

Let me just look. I find this binomial expansion interesting :) thank you so much. I'll call you here if I have further problems ^_^

Answer 19

Sure Monsieur!

Answer 20

Lol this is so easy *facepalm* haha you're great, apoorv!

Answer 21

Let me try to do a problem with this method. Hmm.

Answer 22

\( \color{Black}{\Rightarrow (a + b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5 }\)

Answer 23

Well, just checked if I was right, RIGHT!

Answer 24

Sir, thou art absolutely correct!! Great!!! =]

Answer 25

=) =)