Question

Can someone explain binomial expansion to me please?

Answer 1

you would be best off googling it and find a clear explanation that you like

Answer 2

In simple high school terms :-)

Answer 3

wiki is a good first start
then there are proofs
then there is lots of stuff out there on pascal's triangle

Answer 4

Binomial Theorem

For any value of n, whether positive, negative, integer or non-integer, the value of the nth power of a binomial is given by:


There are many binomial expansion applications in physics.

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Binomial Expansion

For any power of n, the binomial (a + x) can be expanded



This is particularly useful when x is very much less than a so that the first few terms provide a good approximation of the value of the expression. There will always be n+1 terms and the general form is:


** Examples
Applications

Kinematic time dilation Gravitational time dilation
Kinetic energy Electric quadrupole field
Relativity factor gamma ...
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Binomial Expansion Examples

The binomial expansion is a useful example of a series. Some common examples of its application are:



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Answer 5

Yeah I didn't understand wikipedia's explanation

Answer 6

I'm really sorry but i honestly don't understand it yet! Lol...

Answer 7

credits to the website: http://hyperphysics.phy-astr.gsu.edu/hbase/alg3.html

Answer 8

here is a fairly simple one, especially for expanding
\[(a+b)^n\]
http://www.krysstal.com/binomial.html

Answer 9

here is an easier one !WAYY EASY
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_BinomialExpansion.xml

Answer 10

@naadirah do you know how to make pascal's triangle?

Answer 11

i think the point is that you can find an explanation that is complicated or easy for you to understand, but there is still some work to be done. you will not understand it until you read and do a couple of problems. it is not as if someone will be able to say
"it is thus and such"
and you will go
"oh ok i get it"
it requires some work

Answer 12

Oh thank you so much @satellite73! This web page seems quite simple and easy to understand... Still reading it so just give me a minute. Thanks to Izzy25 as well :) (Yeah I understand Pascals's triangle)

Answer 13

then if you understand how to make it we can do a simple example of expanding
\[(a+b)^5\] go down to the fifth level of pascals triangle and read off the numbers
they are
1 5 10 10 5 1
so you know that
\[(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5\]

Answer 14

the pattern should be clear; the exponents have to add to 5. why this works is actually fairly interesting.
and then there is a matter of computing
\[\dbinom{n}{k}\] those coefficients, for larger values. (you might have seen this written as nCk, same thing

Answer 15

and also interesting is why the construction of pascal's triangle gives you the numbers you want. so there is actually a fair amount of math here to be studied

Answer 16

Definitely, I think once I read further on this I'll begin to understand properly how it's all linked together - like Pascals's triangle and Newtons formula. Thanks for all your help :)

Answer 17

Look for youtube clips too to help demonstrate it if you are more of a visual learner

Answer 18

Yep :) Good idea....