Binomial theorem:
[tex](x-y)^n=\displaystyle\sum_{k=0}^n\binom nkx^k(-y)^{n-k}[/tex]
The term with [tex]x^4y^{18}[/tex] corresponds to [tex]n=18+4=22[/tex] and [tex]k=4[/tex] (or [tex]k=18[/tex], since [tex]\dbinom nk=\dbinom n{n-k}[/tex]).
So, the coefficient of this term is
[tex]\dbinom{22}4(-1)^{18}=\dbinom{22}4=\dfrac{22!}{4!(22-4)!}=7315[/tex]
