This simple Hack will help you solve this problem in Seconds? | NO Calculators Allowed

[CjqNslXUcM]

I like the difference of squares, I use it a lot when multiplying larger numbers where the difference is even. For example 27 x 33 = (30+3)(30-3) = 30^2-3^2 = 900-9 = 891

[Teamstudy]

Easiest question ever seen on your channel!!

[gavintillman]

Quicker to visualise as sun of geometric progression, can do it in one’s head instantly. Think of 2021 as 2022-1 and you have the sun of a GP with initial value 1, constant ratio 2022 and number of terms 2, so solution is 1+2022 ie 2023.

[rilian]

can be generalized to
(a+1)^2 - 1
= a+2
a

[ConorChewy]

I didn't spot the difference of squares route, I thought about it geometrically.
Imagine a grid of points 2022×2022, and then you take away the bottom corner point, you'd be left with a block of points 2022 tall and 2021 wide and a single strip of 2021 points on the side, so dividing by 2021 would give 2022+1=2023.

[addison_reilly]

This can also be done very quickly with some simple algebra,
Let x=2021
So:
(2022²-1)/2021
Becomes:
((x+1)²-1)/x
Then, by expanding out (x+1)² we get:
(x²+2x)/x
And now, we can factor out the x:
(x(x+2))/x
So that the x on the top and bottom cancel, giving us:
x+2, and since we know x=2021, x+2=2023 :)

[jp-legal]

You can solve it easily with the binomial formula. Setting x = 2021. Than you have ((x+1) ² -1)/x, next step (x²+2x+1-1)/x, same as (x²+2x)/x, divide all through x, then you have (x+2)/1, same as x+2. X is 2021 and add 2 makes 2023.

[parthasarathibehera]

I solved it without watching the video.
Here, what we can actually do here is, we can apply the identity: a² - b² = (a + b)(a - b)
(2022² - 1) ÷ 2021 = (2022² - 1²) ÷ 2021 = ((2022 + 1)(2022 - 1)) ÷ 2021 = (2023 × 2021) ÷ 2021 = 2023
जय श्री राम।

[debdasmukhopadhyay]

So simple, and so nice. Thank you very much. Fantastic.

[ianboard]

This is one of those patterns that appear on SATs - when you see anything in the form a^2-b^2, immediately factor it.

[badalmondal]

I solved it in 0.4 second without seeing the video. The answer is 2022+1 i.e. 2023

[Shankarcreation]

Thank you for giving us a beautiful solution.I've understood these type of sums.Thank you very much for giving us the trick Sir.

[govindashit]

Simple problem.But explainetion is to impressive

[mcorruptofficial]

Great and more importantly actual problem sir, greetings, have been solved in 30 sec about.
Happy New Year 🎆

[Phlebas]

Out of school for a while now, but I'm proud to say I recognized the pattern from the thumbnail and was able to figure it out in my head (took me more than 5 seconds, admittedly)

[albertbatfinder]

I knew from school (not that I ever worked it out) 50 years ago about the difference of two squares. So it was easy. What I don’t like is that for other problems, there must be rules I know and rules I simply don’t know. And if I don’t know, I have no chance. Is the difference of two squares obvious? I don’t think it is. I don’t think it’s anything I could derive off the cuff in an exam situation.

[pavelkyzman]

Excellent thematic video for New Year. You are best! :-)

[georgesadler]

Thank you for another great mathematical video.

[locomotivetrainstation]

There is a trick with square numbers...

So basically lets take the number "394" for example, squaring the number gives 155236

Now, minus by 1 = 155235 = 393 × 395 so that means 394^2 - 1 ÷ 393 = 395

The trick works with any number too

[Tobi-pvcn]

as a engineer, i just ignore the -1 and say the bases are nearly equal, so the solution is 2022. close enough!