1, Ta có:
$(1-x)^{10}=C^0_{10}-C^1_{10}x+C^2_{10}x^2-C^3_{10}x^3+C^4_{10}x^4-C^5_{10}x^5$
$+C^6_{10}x^6-C^7_{10}x^7+C^8_{10}x^8-C^9_{10}x^9+C^{10}_{10}x^{10}$
$=1-10x+45x^2-120x^3+210x^4-252x^5+210x^6-120x^7+45x^8-10x^9+x^{10}$
2. Thay $x=1$ và khai triển $(2-x)^n+x(3+x)^{n-1}=a_o+a_1x+...+a_nx^n$ ta có:
$1^n+4^{n-1}=a_0+a_1+...+a_m \Leftrightarrow 1+4^{n-1}=65537 $
$\Leftrightarrow 4^{n-1}=655436 \Leftrightarrow n-1=8 \Leftrightarrow n=9$
Ta có: $(2-x)^9+x(3+x)^8=\sum_{k=0}^{9}C^k_92^{9-k}(-x)^k+x\sum_{k=0}^{8}C^k_82^{8-k}(-x)^k$
Suy ra: $a_4=C^4_92^5+C^3_83^5=17640$