goi y nha A=1/2.(3^2-1)(3^2+1)....(3^32+1)

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

Ta có

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

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

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

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

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

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

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

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

bài này nâng cao 6 có đấy

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

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

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

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

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

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

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

A = 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

thanks 2 bạn

   3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1)

=(2²-1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1)

=(2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1)

=(2⁸-1)(2⁸+1)(2¹⁶+1)(2³²+1)(2⁶⁴+1)

=(2¹⁶-1)(2¹⁶+1)(2³²+1)(2⁶⁴+1)

=(2³²-1)(2³²+1)(2⁶⁴+1)

=(2⁶⁴-1)(2⁶⁴+1)

=(2¹²⁸-1)

Nếu thấy đúng thì thích cho mình nha

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

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

\(=\left(3^4-1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)

\(=\left(3^{16}-1\right)\left(3^{16}+1\right)-3^{32}=3^{32}-1-3^{32}=-1\)

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

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

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

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

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

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

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

4294967295

cái này là rút gọn biểu thức

Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\).Ta có : 

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

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

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

...............................................................................

Cuối cùng \(=>2A=3^{64}-1\).

\(=>A=\frac{3^{64}-1}{2}\)

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

\(\Rightarrow2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

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

\(=...........................................\)

\(=\left(3^{32}-1\right)\left(3^{32}+1\right)=3^{64}-1\)

\(\Rightarrow A=\frac{3^{64}-1}{2}\)

bạn ơi!! 2⁸ +1 chứ, bn xem lại đề cấy