Question

两题有关乘法公式的计算题（初一下苏教版）

Answer 1

(2+1)*(2^2+1)*(2^4+1)*(2^8+1)-2^16

=(2-1)(2+1)*(2^2+1)*(2^4+1)*(2^8+1)-2^16

=(2^2-1)(2^2+1)*(2^4+1)*(2^8+1)-2^16

=(2^4-1)(2^4+1)*(2^8+1)-2^16

=(2^8-1)(2^8+1)-2^16

=2^16-1-2^16

=-1

(10+1)(10^2+1)(10^4+1)(10^8+1)...(10^32+1)

(10+1)(10^2+1)(10^4+1)(10^8+1).(10^32+1)

=1/9*(10-1)(10+1)(10^2+1)(10^4+1)(10^8+1)...(10^32+1)

=1/9*(10^2-1)(10^2+1)(10^4+1)(10^8+1)...(10^32+1)

==1/9*(10^4-1)(10^4+1)(10^8+1)...(10^32+1)

=...

=(10^64-1)/9