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
I discovered this very early. When I looked at the thumbnail I already had 2022^2 - 1 translated into 2021*2023. Then the solution was very easy: 2021*2023/2021=2023.
doing 27*30 which most people can get pretty damn fast since it is similar to doing 3^4 but instead of multiplying 27*3 you are multiplying by 30, and adding 27*3 which is exactly like 3^4 is faster for me
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.
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.
@@williammbollombassy1778 I understand you're French but if you want us to understand you gotta speak english. I'm Italian but I'm not writing: "Io ho avuto la tua stessa idea non ci credo", no, I write it in order to make others understand
@@HackedPC Idk whether I am right but here's ur solution it is very well known that we can write a^2+1/a^2=(a-1/a)^2+2, just replace it 2(a-1/a)^2-(a-1/a)-5 (-7+2=5) let a-1/a=x 2x^2-x-5 by solving this quadratic expression u will get x=(1-sqrt(41))/4 and x=(1+sqrt(41))/4 where x=a-1/a a-1/a=(1-sqrt(41))/4 and a-1/a=(1+sqrt(41))/4 (a-1/a-1+sqrt41/4) and (a-1/a-1-sqrt41/4) thats it btw i am in 9th standard who dont even know quadratic formula lmao XD XD XD XD XD
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.
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 :)
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।
I tried to match with the 2021 from the start. So I did this: (2022²-1)/2021 ={(2021+1)²-1²}/2021 =(2021+1-1)(2021+1+1)/2021 =(2021)(2023)/2021 =2021 जय श्री राम
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
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)
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.
I did it just about as fast, but a slightly different way. I thought of 2022^2 as (2021+1)^2. Actually, I thought of the problem as (n+1)^2-1 all divided by n. Which I simplified as (n^2+2n+1 - 1)/n = (n^2+2n)/n = n+2.
I did this in my head, without any equations. Imagine 2022^2 -1 as a square with sides of 2022, and one point missing at the top right corner. The rightmost column is a column with 2021 points in it. Take this column, rotate it 90 degrees and put it on top of the square. You now have a rectangle with width 2021, and height 2023. How many 2021s in this block? Answer: 2023.
Before watching: difference of 2 squares formula: (2022^2-1) can be written as (2022-1)(2022+1) or 2021*2023. Then 2021 cancels out in the fraction an 2023 remains as the solution. 5 sec was realistic. After watching: yes!
Before watching: 2023. 5 seconds is maybe a little exaggerated, more like 10. After watching: exactly the same solution. Of course it helps to know that you (PreMath) really like that difference of squares formula. 😉
I said that 2022² is the same as (2021+1) ², which expands to 2021² + 2 x 2021 + 1. Inserted into the top line, the 1 cancels out, and you end up with 2021 ( 2021 + 2 ) / 2021
Forty-five seconds, without peeking. I'm getting used to this channel: when in doubt, try the difference-of-squares rule. But how valuable is it to be able to solve problems that are specifically constructed to come apart under specific rules? Is it really a useful measure of intellectual/mathematical skill? There, I said it and I'm glad....
That's certainly slick if you happen to think of it! Or, the 2022² is just 2022×2021+2022, so 2022²-1 is 2022×2021+1×2021… so that over 2021 is 2022+1=2023.
You can write 2022^2 as (2021 +1)^2, the result will be 2022^2 + 2*2021 + 1 then just simplify +1 with -1 and divide for 2021. the result will be 2021+2 = 2023
Can you solution this matter ? A+B+C+D+E+F=20 Provided that you use the numbers from 1 to 19 and do not repeat the use of any number within the solution
There are n numbers of solutions for this!!!😂 U told that we should not repeat the numbers and only use 1to19 not zero and negative number then 1+2+3+7/2+5+11/2=20 (7/2&11/2) lies between 1 to 19 hence satisfies
Damn, I somehow thought I had seen a square in the denominator, too, and so ended up with 4042, via application of the first binomal formula instead of the third ... (but at least I did it in under 30 seconds ;)
Funny, after I did difference of squares I just changed the denominator from 2021 to 2022-1 and cancelled. I'm not used to doing difference of squares with numbers so I didn't think to simplify the numerator.
I solved it in a different way though. I imagined that rather than (2022^2 - 1)/2021 we instead had (10^2 -1)/9 And I got eleven. I tried this method on (5^2-1)/4 and got 6. (X^2 - 1)/(X-1) = X + 1 (X + 1)(X-1) = (X^2 - 1) Aka a proof my method works for any integer. I am not sure if this is an appropriate way of solving this. But it gave me 2023.
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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
Very smart! Very impressive.
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Yes, I do the same
I discovered this very early. When I looked at the thumbnail I already had 2022^2 - 1 translated into 2021*2023. Then the solution was very easy: 2021*2023/2021=2023.
doing 27*30 which most people can get pretty damn fast since it is similar to doing 3^4 but instead of multiplying 27*3 you are multiplying by 30, and adding 27*3 which is exactly like 3^4 is faster for me
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.
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Great example. Thanks!
bro cool
What a beautiful approach!
I don't understand this solution completely, could someone please explain it? Thanks.
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.
I had the same idea goog job bro
Ce que j'ai vu c'est une identité remarquable (a^2-b^2) = (a-b)*(a+b)
@@williammbollombassy1778 I understand you're French but if you want us to understand you gotta speak english. I'm Italian but I'm not writing: "Io ho avuto la tua stessa idea non ci credo", no, I write it in order to make others understand
Easiest question ever seen on your channel!!
@@HackedPC Idk whether I am right but here's ur solution it is very well known that we can write a^2+1/a^2=(a-1/a)^2+2, just replace it
2(a-1/a)^2-(a-1/a)-5 (-7+2=5)
let a-1/a=x
2x^2-x-5 by solving this quadratic expression u will get x=(1-sqrt(41))/4 and x=(1+sqrt(41))/4
where x=a-1/a
a-1/a=(1-sqrt(41))/4 and a-1/a=(1+sqrt(41))/4
(a-1/a-1+sqrt41/4) and (a-1/a-1-sqrt41/4)
thats it btw i am in 9th standard who dont even know quadratic formula lmao XD XD XD XD XD
Glad you think so!
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@@HackedPC wow bro btw can you give me solution and where are u from :)
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.
That's what I did too. x')
Solvable by head within a few seconds.
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 :)
I solved as you 👍👍👍👍👍
Cool
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Upvotes for my fellow Algebra users.
can be generalized to
(a+1)^2 - 1
----------------- = a+2
a
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So simple, and so nice. Thank you very much. Fantastic.
Excellent
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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.
I solved it in 0.4 second without seeing the video. The answer is 2022+1 i.e. 2023
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Me too bro...just after having a look at the thumbnail
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।
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I tried to match with the 2021 from the start. So I did this:
(2022²-1)/2021
={(2021+1)²-1²}/2021
=(2021+1-1)(2021+1+1)/2021
=(2021)(2023)/2021
=2021
जय श्री राम
This is one of those patterns that appear on SATs - when you see anything in the form a^2-b^2, immediately factor it.
Beautiful solution. Thank you, Sir.
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Great and more importantly actual problem sir, greetings, have been solved in 30 sec about.
Happy New Year 🎆
Happy new year!
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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
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)
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.
Simple problem.But explainetion is to impressive
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خیلی خوب، مختصر و مفید 👏👏👏
Excellent! Farsi, a sweet language.
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متشکرم از لطف شما
, good evening sir answer sharing 2023, fine teaching, thank you sir
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I did it just about as fast, but a slightly different way.
I thought of 2022^2 as (2021+1)^2. Actually, I thought of the problem as (n+1)^2-1 all divided by n. Which I simplified as (n^2+2n+1 - 1)/n = (n^2+2n)/n = n+2.
I did this in my head, without any equations.
Imagine 2022^2 -1 as a square with sides of 2022, and one point missing at the top right corner.
The rightmost column is a column with 2021 points in it. Take this column, rotate it 90 degrees and put it on top of the square.
You now have a rectangle with width 2021, and height 2023. How many 2021s in this block? Answer: 2023.
Thank you for another great mathematical video.
Nice resolution on this exercise.
Before watching: difference of 2 squares formula: (2022^2-1) can be written as (2022-1)(2022+1) or 2021*2023. Then 2021 cancels out in the fraction an 2023 remains as the solution. 5 sec was realistic.
After watching: yes!
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Elementary school math, in Serbia. Well known transformation a^2-b^2=(a-b)(a+b)...
tommorow i have math exam about this subject too but we dont square the 1 so it is a bit wired
Excellent thematic video for New Year. You are best! :-)
Wow!
So nice of you.
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You are awesome Pavel😀
Ans : 2023. (Solved in just 1.5 second)
Super
Premath express journey continues 😊👍🌹
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Answer =2023
Found two ways to do it.
let n=2022
hence n^2-1/n-1 = n+1 = 2023 answer or
2022^2-1 = (2022 + 1)(2022-1)/2021)=2023 Answer
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love this hack, thanks for sharing, happy holidays
Happy holidays!
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Very beautiful
very usefull hint sir thanks
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Before watching: 2023. 5 seconds is maybe a little exaggerated, more like 10.
After watching: exactly the same solution. Of course it helps to know that you (PreMath) really like that difference of squares formula. 😉
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Thanks you brother!!!!!!!
You're welcome!
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You are awesome AKD😀
I got the answer in a second nice thank you
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as a engineer, i just ignore the -1 and say the bases are nearly equal, so the solution is 2022. close enough!
I said that 2022² is the same as (2021+1) ², which expands to 2021² + 2 x 2021 + 1. Inserted into the top line, the 1 cancels out, and you end up with 2021 ( 2021 + 2 ) / 2021
Forty-five seconds, without peeking. I'm getting used to this channel: when in doubt, try the difference-of-squares rule.
But how valuable is it to be able to solve problems that are specifically constructed to come apart under specific rules? Is it really a useful measure of intellectual/mathematical skill?
There, I said it and I'm glad....
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You are awesome William😀
I've been thinking the same thing for a while now but didn't say it.
I made a=2021 and worked with a+1. Not quite 5 seconds, but easily less than one minute.
Alternatively you can use distributive law
(2021 + 1)*2022 / 2021 - 1/2021
=2021*2022/2021 + 2022/2021 - 1/2021
=2022 + 1 = 2023
That's certainly slick if you happen to think of it! Or, the 2022² is just 2022×2021+2022, so 2022²-1 is 2022×2021+1×2021… so that over 2021 is 2022+1=2023.
1:33 - 0:16 = 1:17 = 77 seconds...
Yes, Einstein also came up with general and special relativity in seconds... A lot of seconds...
Superb...
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That was slick. 👍👍👍👍
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Excellent
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Got it, difference of two squares,
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you can write it as ((2022-1)(2022+1))/2021 ( a^2-b^2=(a-b)(a+b)) and 2022-1 is obviously 2021 so we can cancle it out to get 2022+1=2023
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You can write 2022^2 as (2021 +1)^2, the result will be 2022^2 + 2*2021 + 1 then just simplify +1 with -1 and divide for 2021. the result will be 2021+2 = 2023
I’ve done this last year, but in the thumbnail you didn’t put the power 2 to the “1” (I’m not English I don’t know if “power” is correct)
I forgot about the Difference of squares formula, and expanded 2022^2 to (2021+1)^2 but still got the same results though.
Nice!
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Can you solution this matter ?
A+B+C+D+E+F=20
Provided that you use the numbers from 1 to 19 and do not repeat the use of any number within the solution
There are n numbers of solutions for this!!!😂 U told that we should not repeat the numbers and only use 1to19 not zero and negative number then 1+2+3+7/2+5+11/2=20 (7/2&11/2) lies between 1 to 19 hence satisfies
Without using (a+b) ^2formula the answer will get the same as 2023
(2022×2022)-1÷2021
=4088484-1÷2021
=4088483÷2021
Ans =2023
This New Year’s math problem is a little early. Either that or I’m stuck in the past
No worries my friend
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Damn, I somehow thought I had seen a square in the denominator, too, and so ended up with 4042, via application of the first binomal formula instead of the third ... (but at least I did it in under 30 seconds ;)
Would have been cuter to use 2021 -> 2022. As in tonight!
A rare case when I want to like a video without even watching it
Yes ,I can
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Not a bad way to start the year 2022. Take home lesson - things are not bad as they seem.
Funny, after I did difference of squares I just changed the denominator from 2021 to 2022-1 and cancelled. I'm not used to doing difference of squares with numbers so I didn't think to simplify the numerator.
thanks!
I think rewriting 2022^2 to 2022*2021+2022 is simpler and thus nicer.
GooD!
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You are awesome AJ😀
By using a²-b²=(a+b)(a-b) we can cancel 2021 and the remaining is (2022+1)×1/1 which is 2023
A small second for you, but one giant second for me
Simpler:
2022^2 = 2022x2022 = 2021x2022 + 2022, hence:
2022^2 -1 = 2021x2022 + (2022-1) = 2022x2021 + 2021 = 2023x2021.
Hence result = 2023.
#factoring #factor #binomial #polynomial
I used my phone instead of a calculator. Wasn't it allowed either?
Elegant!
2023 as u treat 2022 as x and make the equation (2022+1)(2022-1) then cancel out 2021 to get 2023
If you did not recognise difference of two square, you did not pass year 9 (junior high) math.
I solved without solving, its as basic as we can know the answer as postulate
Before watching the video: 2023.
He - do this sum in 5 second
Meanwhile he - do it in 1:48 min 😂
But i got the answer 2023 by same method before clicking this video 😅
Hedef 2023! Hauhauhau! Ulan bu niye keşfetime düştü, amk!
a2-b2=(a+b)(a-b)
great
It took a minute but it was fairly simple. Let a be 2021. So, the thing becomes
a*a + 2a +1 -1 = ax
x = a * (a+2) /a = a+2 = 2023
Good to know. This type of problem occurs all the time…NOT
2023. 20 seconds
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Instead of using formula as basis for "tricks" and "hacks", he should try to teach people systematically in maths.
5 seconds calculators not allowed? Oh I feel so challenged, I must click. Actually no.
Slick!
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solved it immediately ;)
Done.
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Здорово , сначала стопор. А потом , как дважды два.
Difference of 2 squares. 2023
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2023 by sqare method
Excellent Ranveer
0.3 Seconds ✔
Without seeing video ON 0.3 SECOND I GOT ANSWER 2023
😂this was so easy literary took spilt split second btw I remember this formula form my 7 or 8th class🤔
A geometry solution instead of (boring) algebra: ruclips.net/video/DZxcrRuRKGY/видео.html
2022 +1...fraction of a second.
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See next year for the answer.
（2022-1）（2022+1）/2021=2023
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👍
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2023 is my answer. I solved it in my head. Let’s see if I am right.
I solved it in a different way though. I imagined that rather than (2022^2 - 1)/2021 we instead had (10^2 -1)/9 And I got eleven. I tried this method on (5^2-1)/4 and got 6. (X^2 - 1)/(X-1) = X + 1
(X + 1)(X-1) = (X^2 - 1)
Aka a proof my method works for any integer.
I am not sure if this is an appropriate way of solving this. But it gave me 2023.
Without watching it all. Pausing at the 4th sec. 2022^2-1/(2021) =(2022-1)(2022+1)/2021=(2021)(2023)/2021 =2023
thumbnail has a difrent question then the one he solved