Question

rút gọn biểu thức :

3(2^2+1)(2^4+1)(2^8+1)(2^16+1)

Answer 1

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

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

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

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

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

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

Answer 2

3.(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2²-1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2⁴-1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2⁸-1).(2⁸+1).(2¹⁶+1)

=(2¹⁶-1).(2¹⁶+1)

=2³²-1