Đáp án+Giải thích các bước giải:
Bài 7:
`a) (a+b+c)^2-(a-b-c)^2`
`=[(a+b+c)-(a-b-c)].[(a+b+c)+(a-b-c)]`
`=(a+b+c-a+b+c).(a+b+c+a-b-c)`
`=(2b+2c).2a`
`=4ab+4ac`
`b) (a-b+c)^2`
`=[(a-b)+c]^2`
`=(a-b)^2+2.(a-b).c+c^2`
`=a^2-2ab+b^2+2ac-2bc+c^2`
Bài 6:
`S=(2^2+1).(2^4+1).(2^8+1).(2^(16)+1). (2^(32)+1)`
`3S=3.(2^2+1).(2^4+1).(2^8+1).(2^(16)+1). (2^(32)+1)`
`=(2^2-1).(2^2+1).(2^4+1) .(2^8+1).(2^(16)+1). (2^(32)+1)`
`=(2^4-1).(2^4+1).(2^8+1).(2^(16)+1). (2^(32)+1)`
`=(2^8-1) .(2^8+1).(2^(16)+1). (2^(32)+1)`
`= (2^(16)-1).(2^(16)+1). (2^(32)+1)`
`= (2^(32)-1).(2^(32)+1)`
`=2^(64)-1`
`-> S=(2^(64)-1)/3`