By the binomial theorem,
[tex](x+y)^8=\displaystyle\sum_{n=0}^8\binom8nx^{8-n}y^n[/tex]
The [tex]x^3y^5[/tex] term occurs for [tex]n=5[/tex]; this gives the term
[tex]\dbinom85x^{8-5}y^5=\dfrac{8!}{5!(8-5)!}x^3y^5=56x^3y^5[/tex]
so the coefficient is 56.
