<s>[INST] Finding the coefficient of $x^{10}$ in $(1+x^2-x^3)^8$ The coefficient of $x^{10}$ in $(1+x^2-x^3)^8$. I tried to factor it into two binomials but it became way to long to solve by hand.
 [/INST] $10=2\cdot 5$ or $2\cdot 3+2\cdot 2$. Hence
$$
\binom{8}{5}+\binom{8}{2}\binom{6}{2}=476.
$$
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