Question

(a+2b)^5? expand

Answer 1

uhmm do you know the binomial expansion formula? or are you supposed to do this by brute force?

Answer 2

i dont know it i googled it but wasnt sure

Answer 3

how to use it , thats what i dont get

Answer 4

I think you definitely want to use the binomial expansion here :-)

Do you know anything about it? I don't want to rehash stuff you already know...

Answer 5

http://upload.wikimedia.org/math/5/6/a/56adbffbb111004bd7a996a480de2262.png

Answer 6

no not realy

Answer 7

http://www.youtube.com/watch?v=1pSD8cYyqUo

Answer 8

\[(a+2b)^{5} = a^{5} + 5a^{4}(2b) + 10a^{3}(2b)^{2} + 10a^{2}(2b)^{3} + 5a(2b)^{4} + (2b)^{5} \]

Answer 9

for more info and generic equation, look under Statement of the thorem here: http://en.wikipedia.org/wiki/Binomial_theorem

Answer 10

The binomial theorem says that if you have a binomial such as \((x+y)^n\), you can expand it by systematically multiplying the binomial coefficients by various powers of x and y.

The binomial coefficient is written \[\binom{n}{k} = \frac{n!}{(n-k)!(k)!}\]where \(n!\) means \(n*(n-1)*(n-2)...(2)(1)\)

Then you can write each term of the expansion as \[\binom{n}{k} x^{n-k}y^{k}\] where \(k\) goes from 0 to \(n\).

For us, we've got \(x = a, y = 2b\) and our binomial coefficients are 1,5,10,10,5,1
so that gives us
\[1(a)^5(2b)^0+5(a)^4(2b)^1+10(a)^3(2b)^2+10(a)^2(2b)^3+5(a)^1(2b)^4+1(a)^0(2b)^5\]\[=a^5+10a^4b+40a^3b^2+80a^2b^3+80ab^4+32b^5\]

The real value of this approach comes when you need to expand something big, or just find an individual term. Multiplying out \((a+b)^5\) isn't too difficult if you're careful, but what if you were asked to find the 19th term of \((a+b)^{37}\)?