Question

Rút gọn biểu thức:

\(B=(2^2+1).(2^4+1).(2^8+1).(2^{16}+1)\)

Answer 1

\(B=\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\frac{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\)

\(=\frac{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\)

\(=\frac{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\)

\(=\frac{\left(2^{16}-1\right)\left(2^{16}+1\right)}{3}\)

\(=\frac{2^{32}-1}{3}\)