Bài 8
a) ( 2 + 1 ).( 2^2 + 1 ).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 2 - 1 ).( 2 + 1 ).( 2^2 + 1 ).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 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
Nếu đúng hãy cho mình + và 5 sao nha >.<

Bài 8
a) cách khác :
Có : 2^32 - 1
= (2^16 - 1 ).( 2^16 + 1 )
= ( 2^8 - 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 2^4 - 1 ).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 2^2 - 1 ).( 2^2 + 1).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 2 - 1 ).( 2 + 1).( 2^2 + 1).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= 1.( 2^2 + 1).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )
= ( 2^2 + 1).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 ) ( ĐPCM )
Vậy 2^32 - 1 = ( 2^2 + 1).( 2^4 + 1 ).( 2^8 + 1 ).( 2^16 + 1 )

Bài 9
d)
D = ( 50^2 + 48^2 + 46^2 + .... + 2^2 ) - ( 49^2 + 47^2 + ..... + 1^2 )
= 50^2 - 49^2 + 48^2 - 47^2 + 46^2 - 45^2 + .... + 2^2 - 1^2
= ( 50 - 49 ).( 50 + 49 ) + ( 48 - 47 ).( 48 + 47 ) + ( 46- 45 ).( 46 + 45 ) +... ( 2 - 1 ).( 2 + 1 )
= 1.( 50 + 49 ) + 1.( 48 + 47 ) + ( 46 + 45 ) + .... + 1.( 2 + 1 )
= 50 + 49 + 48 + 47 + .... + 2 + 1
= ( 50 + 1 ).50/2
= 1275
Vậy........

Bài 8
a, Có 2^32 - 1
= (2^16 - 1).(2^16 + 1)
= (2^8 - 1).(2^8 + 1).(2^16 + 1)
= (2^4 - 1).(2^4 + 1).(2^8 + 1).(2^16 + 1)
= (2^2 - 1).(2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1)
= (2 - 1).(2 + 1).(2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1)
= 1.(2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1)
= (2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1) ( ĐPCM )
Vậy 2^32 - 1 = (2^2 + 1).(2^4 + 1).(2^8 + 1).(2^16 + 1)

b, Có 100^2 + 103^2 + 105^2 + 94^2
= (98+2)^2 + (101+2)^2 + (107-2)^2 + (96-2)^2
= 98^2 + 2.2.98 + 4 + 101^2 + 2.2.101 + 4 + 107^2 - 2.2.107 + 4 + 96^2 - 2.2.96 + 4
= 98^2 + 101^2 + 107^2 + 96^2 + 4.(98+101-107-96) + 4 + 4 + 4 + 4
= 98^2 + 101^2 + 107^2 + 96^2 + 4.(-4) + 4.4
= 98^2 + 101^2 + 107^2 + 96^2 + 4.(-4+4)
= 98^2 + 101^2 + 107^2 + 96^2 + 4.0
= 98^2 + 101^2 + 107^2 + 96^2
Vậy chứng tỏ 100^2 + 103^2 + 105^2 + 94^2 = 101^2 + 98^2 + 96^2 + 107^2