用简便方法计算:101*99*9999

101*99*9999
=(100+1)(100-1)(10000-1)
=(10000-1)^2
=100000000-20000+1
=99980001

()()

=(100+1)*(100-1)*(10000-1)
=(10000-1)*(10000-1)
=10000*10000-2*10000+1
=89980001

=9999*9999
=9999*10000-9999
=99990000-9999
=99980001

原式=(100+1)(100-1)(10000-1)
=（10000-1）^2
=100000000-20000+1
=99980001

=(100+1)*(100-1)*(10000-1)
=(10000-1)*(10000-1)
=10000*10000-2*10000+1
=99980001

(100+1)(100-1)=10^4-1
9999=10^4-1

原式等于
(10^4-1)^2
=(10^4)^2 - 2*10^4 + 1
=10^8 - 2*10^4 + 1
=10000000-20000+1
=99980001