Question

Expand (q + 4n) ^5

Answer 1

@Busterkitten do you know binomial theorem?

Answer 2

binomial theorem?

Answer 3

Do you know the expansion of
\[(a+b)^n\]
?

Answer 4

no

Answer 5

oh which course you are studyin?

Answer 6

do you know combinations?

Answer 7

ok using pascals triangle it the following with a= q and b=4n; once done just substitute them back in. its easier to see the pattern if you use a and b.
Pascals triangle (llok it up if you don't know) has row number five as
1,5,10,10,5,1 ; these are you coefficients
now we list the powers of a and b some just dissappear of couse
\[1a^5b^0+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+1a^0b^5\]
all of the powers of zero dissappear to give
\[a^5+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+b^5\]

Do yo see?

Answer 8

now relplace a with q and b with 4n to get the answer :D

Answer 9

\[(a+b)^n\]=
\[\sum_{r=0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right)a^{n-r}b^r\]

Answer 10

Yes the binomial theorem is also used for combinations as you can see in the sigma notation above its a look up of the row for n and the column for r,

Answer 11

so in our example 5 choose 3 is 10

Answer 12

http://en.wikipedia.org/wiki/Pascal's_triangle

Answer 13

so what's the answer?