Question

Use the binomial coefficient formula to calculate the binomial coefficient for the 8th term in a polynomial expansion when the power of the binomial is 10.

Answer 1

Binomial expansion is:
\[(x+y)^n = \left(\begin{matrix}n \\ 0\end{matrix}\right)x^n+\left(\begin{matrix}n \\ 1\end{matrix}\right)x^{n-1}y+\cdots +\left(\begin{matrix}n \\ n-1\end{matrix}\right)xy^{n-1}+\left(\begin{matrix}n \\ n\end{matrix}\right)y^n\]
where the coefficient of the ith term is given by:
\[\left(\begin{matrix}n \\ i-1\end{matrix}\right)=\frac{n!}{(i-1)!(n-(i-1))!}\]
so just compute:
\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)\]

Answer 2

coefficient=10!/(8!=10x9=90

Answer 3

wouldnt that give the 9th term? notice how coefficient starts at 0 instead of 1.

Answer 4

http://www.wolframalpha.com/input/?i=%28x%2By%29^10
says the coefficient for the 8th term is 120

Answer 5

Just use pascals triangle

Answer 6

sorry but us 10C8=10!/(8!2!)=45