Imagine being such a good teacher that your students literally gasp and shout out in excitement at the insight you gift to them. Talk about inspiring. Mr Woo is a legend.
absolutely blew my mind, great explanation. I feel that understanding the logic behind what I'm learning really helps me grasp the concept, instead of just memorising rules
The amount of sheer glee Eddie Woo derives by just showing them these concepts is infectious. It's incredible how much he loves the subject, and even more so that he can communicate and share where that love comes from with his students.
Eddie's a different kind of math teacher because he was a different math student (in comparison to traditional ones). Eddie, like a lot of people, grew up excelling at the humanities and social sciences but struggling with math. However, while he was in college, he met professors and such that helped him to shift the way he thought about math. Plus, he was able to figure out how he learned it. Unfortunately, most of us weren't that lucky. Kids today are lucky -- because they have access to a lot more resources and such.
@@sergiodongala Well, if you type in x^2 into Desmos graphing calculator it won't give you the picture of a square. It gives you the graph of a parabola.
That's why we start by teaching multiplication of two binomials with algebra tiles and the box method. It's so beautiful to see the conceptual diagram continues to work. But to hear this group get so excited about seeing the "why" behind the algorithm they know is awesome!
Absolutely blew my mind! This is why I love math so much. A lot of people hate it because they think it's all just about numbers, but when you put tangible context to it, it becomes something entirely different and meaningful.
THIS is tge teacher i aspire to be if i ever really become one. Energetic, passionate, logical, and names my students gasp in excitement!! Im in grade 11 and my class is so dead. They hate math but next year, its not compulsory to take it so hopefully my class is a lot more happy and willing to learn. Its hard to feel motivated when the people around you hate that room so much
I'm 32 years old, and this is the first time I've ever seen the completing the square rule being shown geometrically! I learnt the rule in school and understood it in terms of the coordinates of the turning point of the parabola on a Cartesian plane. My mind was as blown as those kids in your class when I saw the rule visually represented!
actually, if you look at some old books, they show it this way. Lots of work was done in ancient Persia with quadratics and completing the square with using area for farmland, thus the area model. I didn't learn the area model until I became a Math teacher.
I actually cried at the kids gasping! I am a teacher (not maths) trying to home educate my autistic son. We are learning complete the square just now and this video made me quite emotional.
You are the most insightful teacher I have ever had the pleasure to watch. I have even caught myself watching you teach subject matter I thought I already knew, mostly because your approach is so uniquely eye-opening (and entertaining). And then BAMM! You hit me with an idea I never saw coming...like you did in this video (eg, completing the squares). I'm all smiles. Thanks.
Great video! Are these high school students? They seem very enthusiastic, excited, and engaged in learning math. I wish my community college students would get this excited about learning math…
These are high school students. This is just like my class was in HS. It's worth noting that maths is not compulsory in years 11 and 12 in NSW(Aus) so these kids chose the class and want to be there.
twistedblktrekie Think about how our generation was taught. Teachers today are basically in new territory and its a difficult thing. Also on the new scheduling some students will go as much as 9 months without having a math class. Also teachers are left with no extra time to review basics. You have to have very motivated students.
@@milly4543 It is sad that math is not compulsory in years 11 and 12 in Australia. Math is something that is so fundamentally important to developing a sense of logic, especially as an early adult. I think policy makers of the future should keep this in mind.... math is very useful, the most important thing you will ever learn.
Roon Station You have to keep in mind that some people, even successful people won’t need trigonometry, calculus, complex numbers, or even geometry to get through most of life’s problems. In fact, math is entirely useless without being able to apply it. We always apply math in physics and economics (because what else is there other than physics and economics). Algebra is one of the most useful concepts there is and is easy to apply. Want to know how much wood you’re going to need for a month? Construct a function of demand. Now higher levels of math are almost always used in the stock market, physics, and other really complicated stuff, but only a small minority deal with this stuff.
I love your charisma and expertise. I'm showing this video to my students since this made me get so excited about solving quadratic equations by completing the square.
Great video Eddie. This is from al-Khwarizmi, circa 820 AD. If he had understood Brahmagupta as well as Euclid he could have solved this problem with a circle to solve for both positive and negative solutions.
As I've dived into math on my own I've learned that we are taught things out of order so all the formulas we learn just seem like tricks rather than the obvious conclusion to something we were taught. We should've been taught the geometry of this formula before the algebra
We all know Eddie added in a stock "amazed classroom sound" They were really all sitting there with their heads rested in their hand waiting for the bell to go
I used the geometric representation in my credentials interview today!! I did it algebraic representation first and when the professor asked me where did the (b/2)^2 came from, I demonstrated it geometrically.
Late night browsing on the tube; I studied math at a top tier university, I never knew why it was ever called completing the square. I never did bother to ask. Lol. BUT, I completely get it now. awesome. lol. Algebra is nice, and efficient, but this is pretty amazing. lol. Get this man to 100 mil subs!! The future depends on it. lol. make people like math again. Because it is beautiful
Both of the math teachers I've had this year were awesome- 1st dude was super chill and clearly and efficiently explained every concept to us. Miss that guy. Second teacher that I just got recently is enthusiastic and incredibly helpful. She makes sure we don't ever have any unanswered questions and clearly loves her job. Now I want this dude too. How much is a plane ticket to Australia? I'm gonna be completely honest- I hate math. it just isn't for me. I'm actually pretty good at math once I know the formulas (I mean duh, that's kinda how math and math classes work) but I don't get any joy from it. And yet somehow the teachers keep me thoroughly engaged. Pay these people more please
This is great stuff and the more ways we can explain things, the greater the likelihood that (a) we find at least one way that works for us and (b) those explanations can combine to deepen understanding. There does need to be caution of course in that geometrical proofs might not always tell us the *whole* story. We live in a physical world where the distance between two points is positive, and an area is positive, and negative distances and areas don't really make sense. So we can neatly see here, for example, that a solution is x = 3, because we make up the side length of (x + 5) = 8 and therefore get an area of 64. However, this might lead us to easily ignore or discard the other solution x = -13, because (-13 + 5) is -8, (-8)² is also 64, and therefore -13 is also a solution to the original equation. It might be possible to somehow geometrically represent that solution by working in terms of displacement and saying "well if we treat moving to the right as positive, and we move x units right, we can then move 13 units left, and do the same in the up/down direction, and construct some other square that might show the relationship, but to be honest, I haven't thought it through fully and to be honest, don't want to, because it seems like more work than is necessary. I'm taking nothing away from an excellent visualisation and if it gets you further than you would otherwise be, that's fantastic, I'm merely saying depending on level, one has to be mindful of the limitations of a particular explanation.
I agree with you. I'm no math genius but he is converting between 1D and 2D to his convenience which is kinda breaking the essence of it... I think its just a cool coincidence, geometrically speaking...
Mr. Woo, this is an excellent video showcasing stellar teaching. You sort of mentioned wondering why you didn't introduce this visual demonstration of Completing the Square prior to this lesson. My question is: would you recommend doing this visual demonstration of Completing the Square before drilling the algebraic strategy (to provide more context for the formula), OR do you think the order which you did here (visual proof after algebraic drilling) makes the visual proof more profound and meaningful? I'd love to hear your thoughts here, cheers!
So if I have a equation like x^3 + x^2=50 Could I complete the cube? I would multiply the x^2 term by 1/3 to break the block into three pieces to extend in three dimensions, then I would cube the value to complete the cube. Does this check out? Can this be applied towards higher dimensions of space?
There is a cubic formula, and a quartic formula, but the quartic is the end of the line, when it comes to solving a general polynomial with only using arithmetic, powers, roots, and complex number math. Galois proved there is no general quintic, or anything beyond. Here's the perfect cube identity: (u+v)^3 = u^3 + 3*u^2*v + 3*u*v^2 + v^3 If we can get a cubic equation to look like this, then it can be a complete cube after all. It turns out we can do this form any cubic equation. Given any cubic equation: a*x^3 + b*x^2 + c*x + d = 0, we can preprocess it to reduce it to only two parameters. A trivial step is dividing every term by 1. A less-obvious step, is to shift the cubic horizontally, until the squared term disappears. The simplified form is called a monic depressed cubic. We can do this, by defining t such that x = t - b/(3*a). After substituting and expanding, we get t^3 + p*t + q = 0. The parameters p & q, will be combinations of the original coefficients. I'll leave it to you to derive their expressions. So now we have a monic/depressed cubic, and need to line it up with the perfect cube identity. Start by letting t = u+v. Then, factor out 3*u*v from the middle two terms: (u+v)^3 = u^3 + 3*u^2*v + 3*u*v^2 + v^3 (u+v)^3 = u^3 + 3*u*v*(u+v) + v^3 t^3 = u^3 + 3*u*v*t + v^3 Shuffle everything left: t^3 - 3*u*v*t - u^3 - v^3 = 0 Line up p & q, to match this equation: p = -3*u*v q = -u^3 - v^3 Solve top equation for u: u = -p/(3*v) Substitute: q = -(-p/(3*v))^3 - v^3 Multiply everything by v^3: q*v^3 = (p/3)^3 - v^6 Shuffle left: v^6 + q*v^3 - (p/3)^3 = 0 Let w = v^3, and it becomes a quadratic: w^2 + q*w - (p/3)^3 = 0 Solve for w: w = -q/2 +/- sqrt((p/3)^3 + (q/2)^2) The + sign becomes u^3, and the - sign becomes v^3. The two cube roots of each w, add together to find t. t = cbrt(-q/2 + sqrt((p/3)^3 + (q/2)^2)) + cbrt(-q/2 - sqrt((p/3)^3 + (q/2)^2)) We're interested in all 3 cube roots of both expressions. For positive discriminants (D = (p/3)^3 + (q/2)^2), the real cube roots add up to the real and distinct solution, and the complex cube roots add up to the complex solutions. For zero discriminant, the real cube roots add up to the real/distinct solution, and the complex cube roots will be two conjugate pairs that both add up to the same solution. For 3 real roots, all cube roots are non-real, and among them, there will be 3 conjugate pairs adding up to the real solutions. When complete, undo the shift to find x: x = t - b/(3*a)
I think that if students were taught geometric explanations for things like completing the square and multiplying binomials they would understand the concepts much better.
The moment a concept clicks in mathematics, is pure bliss.
ItsThatMilkshake I can't tell you how right you are. One of the reasons maths is my favourite class
Makes the week long struggle feel so worth it
Eurekaaaa!
I love seeing your name at the top of a comments section on a video my teacher sent
nice name
Imagine being such a good teacher that your students literally gasp and shout out in excitement at the insight you gift to them. Talk about inspiring. Mr Woo is a legend.
AGREE !!!!!!!!!!🏅
absolutely blew my mind, great explanation. I feel that understanding the logic behind what I'm learning really helps me grasp the concept, instead of just memorising rules
That understanding is the essence of math. Memorizing rules is just computation and calculation, and machines are better at that.
That is so true! Most minds can memorise but enquiring minds need to know why!
The amount of sheer glee Eddie Woo derives by just showing them these concepts is infectious. It's incredible how much he loves the subject, and even more so that he can communicate and share where that love comes from with his students.
Eddie's a different kind of math teacher because he was a different math student (in comparison to traditional ones). Eddie, like a lot of people, grew up excelling at the humanities and social sciences but struggling with math. However, while he was in college, he met professors and such that helped him to shift the way he thought about math. Plus, he was able to figure out how he learned it. Unfortunately, most of us weren't that lucky. Kids today are lucky -- because they have access to a lot more resources and such.
the students are so excited to have it click. awesome.
So, "completing the square" is about literally completing the square. I have never seen such an explanation ! Mind blown !
Me too. I did not know why they call this way. I wish i had a teacher like him.
@@sergiodongala should be in your algebra textbook though
@@sergiodongala Well, if you type in x^2 into Desmos graphing calculator it won't give you the picture of a square. It gives you the graph of a parabola.
That's why we start by teaching multiplication of two binomials with algebra tiles and the box method. It's so beautiful to see the conceptual diagram continues to work. But to hear this group get so excited about seeing the "why" behind the algorithm they know is awesome!
Absolutely blew my mind! This is why I love math so much. A lot of people hate it because they think it's all just about numbers, but when you put tangible context to it, it becomes something entirely different and meaningful.
Just two words........
Absolutely brilliant!
This makes so much sense and it is so awesome. I wish I could just watch TH-cam videos all day to learn instead of going to college
i think you can...
THIS is tge teacher i aspire to be if i ever really become one. Energetic, passionate, logical, and names my students gasp in excitement!! Im in grade 11 and my class is so dead. They hate math but next year, its not compulsory to take it so hopefully my class is a lot more happy and willing to learn. Its hard to feel motivated when the people around you hate that room so much
I'm 32 years old, and this is the first time I've ever seen the completing the square rule being shown geometrically! I learnt the rule in school and understood it in terms of the coordinates of the turning point of the parabola on a Cartesian plane. My mind was as blown as those kids in your class when I saw the rule visually represented!
actually, if you look at some old books, they show it this way. Lots of work was done in ancient Persia with quadratics and completing the square with using area for farmland, thus the area model. I didn't learn the area model until I became a Math teacher.
@@eugene188 In that case! plz try teaching your students like this. They'd thank you for life.
I actually cried at the kids gasping! I am a teacher (not maths) trying to home educate my autistic son. We are learning complete the square just now and this video made me quite emotional.
❤❤❤❤ i am crying reading this.. i feel like a junk in the world, i dont see the suffering of the world..
MINDBLOWN!!! I was literally screaming with the students as if I was in the class. Thanks for the explanation.🙌👍
You sir is the best teacher ever.. the students should consider themselves really really lucky to have a teacher like you
I have gone my whole life hearing the expression 'completing the square', and never knew what it was about. What lousy maths teachers I had!
Mrs Brady has a lot to answer for.
Maybe they did, maybe you weren't present.
@@fredd298 and maybe not, like what most teachers do in my country, sad..
You are the most insightful teacher I have ever had the pleasure to watch. I have even caught myself watching you teach subject matter I thought I already knew, mostly because your approach is so uniquely eye-opening (and entertaining).
And then BAMM! You hit me with an idea I never saw coming...like you did in this video (eg, completing the squares).
I'm all smiles. Thanks.
This is absolutely brilliant for visual learners ! Thank you so much....this is fabulous for helping my son to understand. You are awesome.
Great video! Are these high school students? They seem very enthusiastic, excited, and engaged in learning math. I wish my community college students would get this excited about learning math…
Joshua Britt
This is just like my maths class
These are high school students. This is just like my class was in HS. It's worth noting that maths is not compulsory in years 11 and 12 in NSW(Aus) so these kids chose the class and want to be there.
twistedblktrekie Think about how our generation was taught. Teachers today are basically in new territory and its a difficult thing. Also on the new scheduling some students will go as much as 9 months without having a math class. Also teachers are left with no extra time to review basics. You have to have very motivated students.
@@milly4543 It is sad that math is not compulsory in years 11 and 12 in Australia. Math is something that is so fundamentally important to developing a sense of logic, especially as an early adult. I think policy makers of the future should keep this in mind.... math is very useful, the most important thing you will ever learn.
Roon Station You have to keep in mind that some people, even successful people won’t need trigonometry, calculus, complex numbers, or even geometry to get through most of life’s problems.
In fact, math is entirely useless without being able to apply it. We always apply math in physics and economics (because what else is there other than physics and economics).
Algebra is one of the most useful concepts there is and is easy to apply. Want to know how much wood you’re going to need for a month? Construct a function of demand.
Now higher levels of math are almost always used in the stock market, physics, and other really complicated stuff, but only a small minority deal with this stuff.
The best video and representation of the applied information I have seen on the subject. You have blessed me today, thank you Mr. Woo.
I love the energy and enthusiasm with which concepts are made clear!
I love your charisma and expertise. I'm showing this video to my students since this made me get so excited about solving quadratic equations by completing the square.
Wow, that's what I am exactly looking for. the practical meaning of "completing the square". Thank you.
the reactions of your students are so wholesome ❤
Great video Eddie. This is from al-Khwarizmi, circa 820 AD. If he had understood Brahmagupta as well as Euclid he could have solved this problem with a circle to solve for both positive and negative solutions.
Bloody brilliant!! What a fabulous and inspiring teacher!👏🏻👏🏻👏🏻
As I've dived into math on my own I've learned that we are taught things out of order so all the formulas we learn just seem like tricks rather than the obvious conclusion to something we were taught. We should've been taught the geometry of this formula before the algebra
Wow, U are a very enthusiastic teacher.
God bless Sir.
What a great Match Teacher, this is so enlightening.
Dislikes are from the triangle people. Thank you for the visual Eddie. You're a great teacher.
Just amazing. Thank you. 20years after failing my GCSE math I'm retaking.
Good luck!
WOW !!!! I'm going to point my daughter to your lessons !!!!
and majority of students are in debt while never even knowing these type of beauty in math. really sad!
This man just made Algebra so much easier for me! *Give this man an award!*
The sound of students getting it is the most rewarding feeling ever.
One of the finest teachers in the world!
Pure genius, man. May need to find another word to describe you soon.
Pure genius. Everyone needs a math teacher like this.
2:08 The beautiful lightbulb moment that every teacher loves to experience!
Omg that MathGasm I had was the most mind blowing one I've ever had :D
If only I could get my students to get excited about learning like you have here.
LITERALLY INSANE. STUMBLED UPON THIS VIDEO ( IM IN CLASS 11 AND I AM EXTREMELY GREATFUL TO FIND THIS VIDEO )❤❤❤❤❤❤❤
Brilliant! Love the enthusiasm as well 😊
It's trivial math, but I LOVE your method of teaching! You're awesome ;) ;) I wish I had this kind of teacher at my school :-(
Rudolf Klusal I know it was a year ago lol but it’s not trivial mate, can be used to find the roots of the equation
We all know Eddie added in a stock "amazed classroom sound"
They were really all sitting there with their heads rested in their hand waiting for the bell to go
I used the geometric representation in my credentials interview today!! I did it algebraic representation first and when the professor asked me where did the (b/2)^2 came from, I demonstrated it geometrically.
I wish you were my teacher. No one make us learn this way or explained this way. When i see your videos, i feel my maths teachers were seriously dumb.
2:08 is the climax
2:20 second one
mathgasm, they came twice, he's definitely professional 👏👏👏👏👏
Comparing maths to sex now are we?
yes, since they're mathing
THIS MAKES SO MUCH MORE SENSE THANK YOU EDDIE
Late night browsing on the tube; I studied math at a top tier university, I never knew why it was ever called completing the square. I never did bother to ask. Lol. BUT, I completely get it now. awesome. lol. Algebra is nice, and efficient, but this is pretty amazing. lol. Get this man to 100 mil subs!! The future depends on it. lol. make people like math again. Because it is beautiful
it all suddenly made sense! thank you!!!
Both of the math teachers I've had this year were awesome- 1st dude was super chill and clearly and efficiently explained every concept to us. Miss that guy. Second teacher that I just got recently is enthusiastic and incredibly helpful. She makes sure we don't ever have any unanswered questions and clearly loves her job. Now I want this dude too. How much is a plane ticket to Australia? I'm gonna be completely honest- I hate math. it just isn't for me. I'm actually pretty good at math once I know the formulas (I mean duh, that's kinda how math and math classes work) but I don't get any joy from it. And yet somehow the teachers keep me thoroughly engaged. Pay these people more please
Didn't I see you in itf's videos lol
Do we always add to both sides..? sometimes we subtract.. when do we subtract on the right side?
Brilliant! The reason we come to TH-cam for maths!
This is great stuff and the more ways we can explain things, the greater the likelihood that (a) we find at least one way that works for us and (b) those explanations can combine to deepen understanding.
There does need to be caution of course in that geometrical proofs might not always tell us the *whole* story. We live in a physical world where the distance between two points is positive, and an area is positive, and negative distances and areas don't really make sense. So we can neatly see here, for example, that a solution is x = 3, because we make up the side length of (x + 5) = 8 and therefore get an area of 64. However, this might lead us to easily ignore or discard the other solution x = -13, because (-13 + 5) is -8, (-8)² is also 64, and therefore -13 is also a solution to the original equation.
It might be possible to somehow geometrically represent that solution by working in terms of displacement and saying "well if we treat moving to the right as positive, and we move x units right, we can then move 13 units left, and do the same in the up/down direction, and construct some other square that might show the relationship, but to be honest, I haven't thought it through fully and to be honest, don't want to, because it seems like more work than is necessary.
I'm taking nothing away from an excellent visualisation and if it gets you further than you would otherwise be, that's fantastic, I'm merely saying depending on level, one has to be mindful of the limitations of a particular explanation.
I agree with you. I'm no math genius but he is converting between 1D and 2D to his convenience which is kinda breaking the essence of it... I think its just a cool coincidence, geometrically speaking...
Simply the best..thank you!!
Really impressive sir....I wish if every maths teacher could teach like you...
mind blown!!!!!! if only the teacher we had actually explained it like this I wouldn't be searching the web for hours on how to do these problems. >_
I will never forget this video! (:
Mr. Woo, this is an excellent video showcasing stellar teaching. You sort of mentioned wondering why you didn't introduce this visual demonstration of Completing the Square prior to this lesson. My question is: would you recommend doing this visual demonstration of Completing the Square before drilling the algebraic strategy (to provide more context for the formula), OR do you think the order which you did here (visual proof after algebraic drilling) makes the visual proof more profound and meaningful? I'd love to hear your thoughts here, cheers!
Eddy Woo is a math guru.. he's beautiful!
I can relate to the euphoria the students are experienced because I experienced the same while the math unfolded ❤.
This has saved my GCSE mock today in two hours
Very nice. I will use that with my students this term when solving quadratic equations. Thanks.
thank you for making maths interesting! keep going professor!!
Oh man ! You rocked.
he's like the teacher I never had
I wish I had a teacher like him.
oh my god! this is so cool!! Thanks for sharing this.
He has been nominated for global top prize teacher
i wish i had this teacher as my maths teacher
Eddie's 1 million subscriber video lead me here
NOBEL F'ING PRIZE for teaching! He knocked it out of the park!
Somebody nominate this guy for a Nobel prize
Ohh, mann... Wish i got a teacher like him..... 😢😢😢😢😢
I need those students, if they are cheap enough. Nice vid.
He just shows the beauty of mathematics.
i need this man as my teacher istg
Love the reactions!!
simple and logic thanks from Algeria.
Awesome! Thank you!
Great this really helps a very thick, dyslexic person like myself LOL! But for some reason I have taken an interest in maths because its a challenge!
So if I have a equation like x^3 + x^2=50
Could I complete the cube?
I would multiply the x^2 term by 1/3 to break the block into three pieces to extend in three dimensions, then I would cube the value to complete the cube.
Does this check out? Can this be applied towards higher dimensions of space?
There is a cubic formula, and a quartic formula, but the quartic is the end of the line, when it comes to solving a general polynomial with only using arithmetic, powers, roots, and complex number math. Galois proved there is no general quintic, or anything beyond.
Here's the perfect cube identity:
(u+v)^3 = u^3 + 3*u^2*v + 3*u*v^2 + v^3
If we can get a cubic equation to look like this, then it can be a complete cube after all. It turns out we can do this form any cubic equation.
Given any cubic equation: a*x^3 + b*x^2 + c*x + d = 0, we can preprocess it to reduce it to only two parameters. A trivial step is dividing every term by 1. A less-obvious step, is to shift the cubic horizontally, until the squared term disappears. The simplified form is called a monic depressed cubic. We can do this, by defining t such that x = t - b/(3*a). After substituting and expanding, we get t^3 + p*t + q = 0. The parameters p & q, will be combinations of the original coefficients. I'll leave it to you to derive their expressions.
So now we have a monic/depressed cubic, and need to line it up with the perfect cube identity. Start by letting t = u+v. Then, factor out 3*u*v from the middle two terms:
(u+v)^3 = u^3 + 3*u^2*v + 3*u*v^2 + v^3
(u+v)^3 = u^3 + 3*u*v*(u+v) + v^3
t^3 = u^3 + 3*u*v*t + v^3
Shuffle everything left:
t^3 - 3*u*v*t - u^3 - v^3 = 0
Line up p & q, to match this equation:
p = -3*u*v
q = -u^3 - v^3
Solve top equation for u:
u = -p/(3*v)
Substitute:
q = -(-p/(3*v))^3 - v^3
Multiply everything by v^3:
q*v^3 = (p/3)^3 - v^6
Shuffle left:
v^6 + q*v^3 - (p/3)^3 = 0
Let w = v^3, and it becomes a quadratic:
w^2 + q*w - (p/3)^3 = 0
Solve for w:
w = -q/2 +/- sqrt((p/3)^3 + (q/2)^2)
The + sign becomes u^3, and the - sign becomes v^3. The two cube roots of each w, add together to find t.
t = cbrt(-q/2 + sqrt((p/3)^3 + (q/2)^2)) + cbrt(-q/2 - sqrt((p/3)^3 + (q/2)^2))
We're interested in all 3 cube roots of both expressions. For positive discriminants (D = (p/3)^3 + (q/2)^2), the real cube roots add up to the real and distinct solution, and the complex cube roots add up to the complex solutions. For zero discriminant, the real cube roots add up to the real/distinct solution, and the complex cube roots will be two conjugate pairs that both add up to the same solution. For 3 real roots, all cube roots are non-real, and among them, there will be 3 conjugate pairs adding up to the real solutions.
When complete, undo the shift to find x:
x = t - b/(3*a)
how much you pay the kids for the enthusiasm
I wish you were my maths teacher 😂😭
Don't we all? Lol
Woah that's some really good explanation bro! Doing great!
That's an amazing math teacher.
I think that if students were taught geometric explanations for things like completing the square and multiplying binomials they would understand the concepts much better.
Eddie Woo is the man!
You are the best one i ever had..
i love his dress code
2:11 That's the Mind=Blown moment
Sounds like its from a fantasy. High school maths students exclaiming with surprise and joy while being taught algebra.
big math very big maths 👍🏿 thank you mr woo
Beautiful
Do we always add to both sides..? sometimes we subtract.. when do we subtract on the right side?
Awesome Sir.
i need a video of their reactions :')
very good teacher. thanks
worth watching...
But how do you represent it geometrically when you have powers to the 3 or higher? Cubes and higher dimensions? Thanks.
How would you complete a square when you don't have a square?
How to show using tiles in completing the square when a is not equal to zero?