Question

rút gọn biểu thức

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

Answer 1

Lời giải:

Sử dụng công thức \((a-b)(a+b)=a^2-b^2\)

\(A=3(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)\)

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

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

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

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

Answer 2

3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

=\(\dfrac{3}{2^2-1}\)(2² -1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

=\(\dfrac{3}{4-1}\)(2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)

=\(\dfrac{3}{3}\)(2⁸-1)(2⁸+1)(2¹⁶+1)

=(2¹⁶-1)(2¹⁶+1)

=2³²-1

Answer 3

3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

=\(\dfrac{3}{2^2-1}\)(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

!!!Chúc học tốt!!!