Question

Rút gọn biểu thức

B=3x(2^2+1)x(2^4+1)x(2^8+1).........(2^64+1)+1

Answer 1

A = 3(2²+1)(2^4 + 1)....(2^64 + 1) + 1 

= (2²-1)(2²+1)(2^4 + 1)....(2^64 + 1) + 1 

= (2^4 - 1)(2^4 + 1)....(2^64 + 1) + 1 

= (2^8 - 1).(2^8 + 1)(2^16 + 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^16 - 1)(2^16 + 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^32 - 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^64 - 1)(2^64 + 1) + 1 = 2^128 - 1 + 1 = 2^128. 

Answer 2

B = 3(2²+1)(2^4 + 1)....(2^64 + 1) + 1 

= (2²-1)(2²+1)(2^4 + 1)....(2^64 + 1) + 1 

= (2^4 - 1)(2^4 + 1)....(2^64 + 1) + 1 

= (2^8 - 1).(2^8 + 1)(2^16 + 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^16 - 1)(2^16 + 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^32 - 1)(2^32 + 1)(2^64 + 1) + 1 

= (2^64 - 1)(2^64 + 1) + 1 = 2^128 - 1 + 1 = 2^128.