Question

Binomial theorem help me solve x^5 Y^8 (x+y)^13

Answer 1

I assume you're asking to find the coefficient of the
`x^5y^8` term in the expansion of
`(x+y)^(13)`.

The binomial theorem says that the expansion itself is


`\displaystyle(x+y)^(13)=\sum_(k=0)^(k=13)\binom{13}kx^(13-k)y^k`

and we obtain the
`x^5y^8` term when
`k=8`. So the coefficient of this term would be


`\dbinom{13}8=(13!)/(8!(13-8)!)=1287`