Question

find the 7th term of (x+y)^8

Answer 1

By the binomial theorem, we have

$(x+y)^8=\displaystyle\sum_{k=0}^8\binom8kx^{8-k}y^k$

where $\dbinom8k=\dfrac{8!}{k!(8-k)!}$. The 7th term occurs when $k=6$, which gives

$\dbinom86x^{8-6}y^6=28x^2y^6$