Bài 1:
a) (2+1)(22+1)(24+1)(28+1)(216+1)
=(2−1)(2+1)(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
b) 1002+1032+1052+942=1012+982+962+1072
⇔1002+1032+1052+942−1012−982−962−1072=0
⇔(1002−982)+(1032−1012)−(1072−1052)−(962−942)=0
⇔2.198+2.204−2.212−2.190=0
⇔2(198+204−212−190)=0
⇔2.0=0 (đúng)
Bài 2:
a) 2632+74.263+372
=2632+2.37.263+372
=(263+37)2
b) (502+482+462+...+22)−(492+472+452+...+12)
=502+482+462+...+22−492−472−452−...−12
=(502−492)+(482−472)+(462−452)+...+(22−12)
=(50+49)+(48+47)+(46+45)+...+(2+1)
=50+49+48+47+46+45+...+2+1
=2(50+1).(50−1+1)=1275
Kết luận ...