Question

What is the coefficient of the term x7y in the expansion of (x + y)8?

Answer 1

yas
binomial theorem

ok so

for (a+b)^n
the first term is a^n
2nd term has a^(n-1)
x^7 is 1 less than x^8
we know that it is the 2nd term

to find the nth term of a bionial expansion (a+b)^n
you do,
the nth term is k, so then you do
k-1=z
then
the coeficint of that is

`\left[\begin{array}{ccc}n\\z\end{array}\right] = (n!)/(z!(n-z)!)`

so n=8
k=2
2-1=1
z=1


`\left[\begin{array}{ccc}8\\1\end{array}\right] = (8!)/(1!(8-1)!)`=
`(8!)/((1)(7)!) = (8*7*6*5*4*3*2*1)/(7*6*5*4*3*2*1)=8`
the coefient is 8