The only way to get a term of degree 25 is by taking 3 copies of [tex]x^8[/tex], 1 copy of [tex]x[/tex], and 6 copies of 1. Then the coefficient of [tex]x^{25}[/tex] is
[tex]\dbinom{10}3\dbinom71\dbinom66=\dbinom{10}{3,1,6}=\dfrac{10!}{3!6!}=\boxed{840}[/tex]
