Question

化简999...999(2008个9）*999...999(2008个9）+199...999(2008个9)

Answer 1

999...999(2008个9）*999...999(2008个9）+199...999(2008个9)
=[100...000(2008个0)-1)*999..99(2008个9）+1999...999(2008个9)
=999..999000..000(2008个9)(2008个0)-999..99(2008个9）+1999...999(2008个9)
=999..999000..000(2008个9)(2008个0)+10000..00(2008个0)
=9999..99(2007个9)8000....000(2008个0)

Answer 2

9*9=81,99*99=9801.999*999=998001
可以确定，最后是1，9过后都是8，8后面的有乘数的数位减1个0．而积中的9也是一样，所以因是999...999（2007个9）8000.00（2007个0）1＋199.99（2008个90
后面就不化的太麻烦

Answer 3

设999...999(2008个9）=X
199...999(2008个9)=100...000(2008个0)+999...999(2008个9)
=1+999...999(2008个9)+999...999(2008个9)
原式=X*X+2X+1=(X+1)^2=(10^2008)^2=10^4016

也就是10的4016次方

Answer 4

999...999(2008个9）*999...999(2008个9）+199...999(2008个9)
=999...999(2008个9）^2+99...999(2008个9)×2+1
=[999...999(2008个9）+1]^2
=1000...000(2008个0）^2
=1000...000(4016个0）

Answer 5

设999...999(2008个9)=x
则原题是
x^2+x+1000...000(2008个0)
=x(x+1)+1000...000(2008个0)
=1000...000(4016个0)