Question

what is the expansion of (x+y)^6

Answer 1

\[\sum_{k=0}^{6}\left(\begin{matrix}6\\k\end{matrix}\right)x^{6-k}y^k\]

Answer 2

ok thats not one of the options that they give me

Answer 3

do wyou know what \[\left(\begin{matrix}n\\k\end{matrix}\right)\]means?

Answer 4

nope

Answer 5

\[\left(\begin{matrix}n\\k\end{matrix}\right)={n!\over k!(n-k)!}\]and if that doesn't make sense to you, you can use pascals triangle to find the coefficients, or just do it all by hand (which I don't recommend)

Answer 6

\[(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)\]but that would be really painful

Answer 7

ok know that you brought that up do you know what is the 15th entry in row 15 of pascal triangle. I have no idea how to do that

Answer 8

no I don't know the trick for that, though I'm sure there is one
I just derive it by hand when I use it

Answer 9

oh ok well ill try to find out somewhere else for help

Answer 10

the 15the row in pascals triangle should basically consist of the sequence\[a_k=\{\left(\begin{matrix}15\\k\end{matrix}\right)\}\]from k=0 to 15, so they are actually the same thing I guess...
sorry I couldn't help more, just bump this question and maybe someone can better help you

Answer 11

The fifteenth entry in row fifteen is \[\left(\begin{matrix}15 \\ 15\end{matrix}\right)\]
\[= 15!/(15!(15 - 15)!)\]
since 0! = 1, this evaluates to 1.
This makes sense because the fifteenth term of the fifteenth row is the last term(1)
(This assumes that you count the first row as row 1 not 0)

Answer 12

http://www.wolframalpha.com/input/?i=Expand+%28x%2By%29%5E6