A Nice Olympiads Exponential Mathematics Trick | No Calculator Allowed

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[@rabotaakk-nw9nm]

2:30 4096²-3²=(4096-3)(4096+3)=
=4093•4099=(4000+93)(4000+99)=
=4000²+4000(93+99)+93•99=
=4000²+4000(200-8)+93(100-1)=
=16000000+800000-32000+9300-93=
=16809300-32093=16777207 😁

[@rabotaakk-nw9nm]

… 4093•4099=(4100-7)(4100-1)=
=(4000+100)²+4100(-7-1)+(-7)(-1)=
=16000000+800000+10000-32800+7=
=16810007-32800=16777207 😁

[@rabotaakk-nw9nm]

3:20-5:20 (4000+100-4)²=
=4000²+100²+(-4)²+ 2•4000•100+2•100(-4)+2•4000(-4)=
=16000000+10000+16+ 800000-800-32000=
=16810016-32800=16777216 😁

[@RyanLewis-Johnson-wq6xs]

I got the answer correct.

[@googolian]

Overworked .... 4096 squared is simply 4096x4096 which you could do in primary school

[@RyanLewis-Johnson-wq6xs]

I didn’t use a calculator.

[@juergenilse3259]

2^25-2^24-3^2=
(2*2^24--2^24)-3^2=
2^24*(21)-3^2=
2^24-3^2=
2^(12*2)-3^2=
(2^12)^2-3^2=
4096^2-3^2=
(4096+3)*(4093)=
(4100--1)*(4093)=
4100*4093-4093=
(4000+100)*4093--4093=
4000*4093+100*4093-4093=
16372000+409300-4093=
16781300-4093=
16777207
This looks easier to me than your solution, but our mileage may vary. I would also tend to write 4096^2 as (4100-4)^2 instead of (4000+93)^2, if i woulld go te way of our solution.
4096^2=(4100-4)^2=4100^2-2*4*4100+16=4100^2-8*4100+16=16810000-32800+16=16777200+16

[@satyapriyagogula8334]

Calculation part not impressive.