Question

[Chidethuong]

Rút gọn biểu thức sau:

3.(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)

Answer 1

[Isolde Moria]

( bài này áp dụng hằng đẳng thức \(a^2-b^2=\left(a+b\right)\left(a-b\right)\)

Ta có

\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\)

\(=2^{64}-1\)

Answer 2

[Edowa Conan]

3.(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)

=(2²-1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)

=(2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)

=(2⁸-1)(2⁸+1)(2¹⁶+1)(2³²+1)

=(2¹⁶-1)(2¹⁶+1)(2³²+1)

=(2³²-1)(2³²+1)

=2⁶⁴-1