a^5+5a^4+10a^3+10a^2+5a+1=(a+1)^5
这是杨辉三角型啊
所以
(x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)=
(x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)+1-1=
(x-1+1)^5-1
=x^5-1
a^5+5a^4+10a^3+10a^2+5a+1=(a+1)^5
这是杨辉三角型啊
所以
(x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)=
(x-1)^5+5(x-1)^4+10(x-1)^3+10(x-1)^2+5(x-1)+1-1=
(x-1+1)^5-1
=x^5-1