[Last September, at Hongdae in the breezy morning.] [He finally came...] - There are so many students who were at grade 6. - And they became grade 1 the next year. [The Savior for people who gave up on Math.] [No.1 Math Teacher in popularity vote.] - I have been doing this for 20 years... - I've been studying math from when you were born up until now. [Accumulated number of students - 8.5 million.] - I decided that I will teach class at EBS to my death. [The first private educator who advanced to EBS.] - I will retire even if you don't achieve the grade 1. [The Math-teaching Expert from heaven.] [The Math-teaching Expert from heaven.]
Chung Seung Je - Thank you so much for your time, Teacher. - We know you're busy.
- Oh, don't mention it. - I heard this is the best Youtube channel. - I'm such a big fan of yours.

- Can you sing a song for us before we start? [*He has actually has 2 albums as a singer.]
- Sing a song?
- To warm up your voice [Getting Ready] - Darling Darling, my love, my pretty love. - Please support my songs. - I spent 200 million won on my music video. - Wow.
- Is that your song? - Yes.
- What's it called? - Darling Darling.
- Darling Darling! - It didn't do so well considering 200 million you invested... [Fact] (*Another promotion).
- My Youtube channel is SeungJe Tube. - I only have 100 thousand subscribers. [Please subscribe to SeungJe Tube.]
- So I haven't received my silver button yet. - I have met you before, Jin Kyung. - What? me? where? - 1993, I was at Little Angels Art Hall. - Entrance Number 7! [No.7 Hong Jin Kyung (Designer Hong Mi Hwa)].
- Yes!! I won the Best Pose Award!

- Best Pose Award, yes!
- I was there actually.
- How? how? how? [Baiting]
- I'd stop for now. [W H A T ?]
- I'm so nervous now.
- I won't tell why, but I was there. [Today's Lesson] [Today's Lesson]
- Grudge of 20 million people who gave up on math. [Today's Lesson]
- Grudge of 20 million people who gave up on math.
- FACTORIZATION - The reason we cannot advance to quadratic equation is that we cannot resolve factorization, so we are stuck at linear equation. - OK then, how much time we have, producer? - Until 12...(About 2 hours) - Oh, that's quite a lot. - It is definitely possible. [The journey to the factorization]
1. Polynomial expression
2. Expansion
3. The most basic factorization
4. More advanced expansion
5. Expansion of perfect square expression
6. Factorization of perfect square expression.

[The journey to the factorization]
1. Polynomial expression - Have you heard of 'Polynomial'?
- Yes. - It has multiple equations, right? - There are multiple terms. - Because it has multiple terms, - it means there are many terms. - We should know what the 'term' means first of all. - x + y + 3 - 5x + y^2 - It's like this. - Then how many terms are there? - One, two, three, four, five. - There are five terms. - What distinguishes between each term, - where they are connected via + or -, they are called terms. - So those are connected via +, - those via +, - those via -, - those are connected via +, right? - So the terms are, this is x term, y term, - 3 term, -5x term, and y^2 term, - we call them this way. - What if we have x^2 - 4x + 3, how many terms do we have?

- 3 terms. Yes, there are 3 terms. What we should be careful here is that it's not only 4x. The front sign always follows. So first, there's x^2, then next, -4x, then +3. So there are 3 terms in total. It's not too hard so far, right? Easy, easy. However, how many times x was multiplied for x^2? Twice.
- Multiplied twice, yes. X was multiplied twice, and we call it x^2 (squared). This number 2 is called the 'degree'. It's called 'degree' so we call it second degree. It is a quadratic term for x. 3 means 3rd degree, then?
- It's called a cubic. Cubic, it's the number of times that was multiplied. Y squared means how many times y was multiplied?
- Y twice. Then what is the term for y?
- Quadratic.

- So this is called the quadratic term for y, and we call this the quadratic term for x. What do we call this? We call them terms, terms, terms, right? This is called quadratic terms for x, so those terms are named differently. Looking at the multiplication number, this is called linear term. What do we call this? It has nothing, only a number. People call these CONSTANT. We call it constant term. [Quadratic Term] [Linear Term] [Constant Term]. How many terms are there? There are 3. What we call those terms all together. Because the equation includes multiple terms, it is called Polynomial of x. This is a very important concept. Not too hard, right? No. Do you work as a private tutor? It's been over 20 years the last time I tutored someone. How much do you charge? LOL. I'm curious, really. Ever since I became the online lecturer, I never tutored someone in private. OK.

- Please take care of our channel [Recruiting].
- Please take care of our channel. Let's see how this video goes, if it's a hit. If my subscribers goes up. [*Help us! Subscribers!]
- If my subscribers goes up. Darling Darling~~ [Stumbling].
- Darling Darling~~. Darling Darling My Love~~. Darling Darling My Love. It goes like this. Darling Darling My Love~~. The melody is lit.
- The melody [Satisfied].
- The melody is lit.
- The melody. The melody is almost POLYNOMIAL indeed. It has multiple vibes to it. LOL. Let me explain it first. I must make you able to solve quadratic equation until 12 o'clock. What is the term for this?
- Quadratic. What about this?
- Linear. This?
- Constant. What do we call this as a whole? It is called polynomial expression. For this, the highest term is quadratic, right?

- So people call this quadratic equation among polynomials. So you name it after the highest term within the equation, then? What if there's x^3 here, how many terms are there? - Four.
- Four terms [Four terms]. What is this called in terms of x? - Cubic. Cubic expression = 0, this is called a CUBIC EQUATION. Quadratic expression = 0, that is called QUADRATIC EQUATION. So if we were to study quadratic equation, we must know the name of these things. To do this, we need to know how to do the factorization at first. To do the factorization, we need to know expansion, have you heard about this? [The journey to the factorization]
1. Polynomial expression
2. Expansion
3. The most basic factorization
4. More advanced expansion
5. Expansion of perfect square expression
6. Factorization of perfect square expression

[The journey to the factorization]
2. Expansion - Expansion. It is when we expand things, right? So, for example, a(b+c). Notice that (b+c) has a bracket around it. This empty space means it must be multiplied. This means a will be multiplied to both b and c, right? What is it when b is multiplied by a? ab, expressed like this. When c is multiplied by a? ac, like this. AC~ Have a close look now! Listen carefully. This has two terms. As this is in brackets, there is only one term. This can be seen as one. (b+c) and a are multiplied together. It is not consist of + or -, but multiplication. I told you this before. When we have x - 2x^2y. How many terms are there?
- two. Two, why? A 'term' means when they are connected via + or -.

- However, if we have x^2 X 4y, how many terms are there? - I'm not sure.
- There is only ONE TERM. - If it's multiplication? - There is nothing connected via + or -. - If connected with multiplication, there is only one term - x / 3, how many terms are there?, just one.
- Just one~ [*Term indicates when connected via addition (+) or subtraction (-) ] - When the equation has only one term, it is called a monomial equation - monomial, binomial, and etc. - I finally understand this, phew. - What have I done for the past 45 years... [SIGH]
- What have I done for the past 45 years... - You need to listen carefully - This has two terms, right? - But it has a bracket - Altogether, a is multiplied by (b+c) - So as a whole, - there is ONLY ONE TERM - this a(b+c) is called

- MONOMIAL EQUATION: Brackets - Brackets connected through multiplication - Brackets connected through multiplication, only one term - Brackets connected through multiplication, only one term, MONOMIAL EQUATION - This ab+ac, how many terms?
- Two - There are two, here and here - What do we call this, then? - Polynomial equation - This is monomial equation because it's multiplication - Multiplication = Monomial - This is polynomial equation because it's addition - Addition = Polynomial - So the process of expanding monomial to polynomial, we call it 'EXPANSION' - Therefore, there was only one term, consist of multiplication - As multiplied each term to make the terms into two - Converting monomial to polynomial is called expansion - Reversely, when there were two terms - Converting those to one term - Converting in terms of multiplication - This is today's topic: Factorization - Why the name factorization?

- As the word suggests, it factorizes. It solves into factors. That's why it's called factorization. What is factors? Each connected via multiplication. A is a factor, (b+c) is also a factor. Each connected via multiplication. So have a look. 2 times 3. 6 is expressed as 2 X 3, right? This has been factorized, and it's factorized with the product. This is also called factorization. However, the numbers 2 and 3 are called, in a hard way, prime numbers. So it's factorized by prime numbers as factors, have you heard what it's called? FACTORIZATION in PRIME FACTORS. That was it. Each connected via multiplication is called factors, to expose those factors, the process of converting polynomial equation to monomial equation is called what? Simply? Simply called 'Factorization' [Expansion] [Factorization]

- Expansion is easier then. Expansion is much easier. Therefore, the first point where there comes the people who gave up their math, [FOCUSED].
- at this point? It's Factorization. When do we learn this? The first semester of Grade 9. That's right. [Right on spot].
- I gave up then as well. So what are we gonna do today? [*Factorization].
- Converting a polynomial equation with multiple terms into - monomial equation with single term, - we will undergo the process of solving the quadratic equation. The reason that we must convert to solve this will be discussed later. As this is the basic tool for solving a quadratic equation, - Being familiar with this will be our today's goal, everyone. - Fighting!
- Thank you. [The journey to the factorization].
1. Polynomial expression.
2. Expansion.
3. The most basic factorization.
4. More advanced expansion.
5. Expansion of perfect square expression.
6. Factorization of perfect square expression.

3. The most basic factorization. Let's continue. -3(x+2y). This is in terms of multiplication. To expand this, we must convert it in terms of addition. When we multiply -3 to each, it will be -3x. What if we multiply this and this, it's -6y. Good.
- That's right. So what do you call this conversion? Expansion.
- Expansion, yes. So factorization is to reverse this process, right? Let's try it, we should know how.
- Let's do it. This is how you do it. There are two terms. The factor which is in each term. The factor which is multiplied to each term. Here is 3 and this has 3 in it, right? Yes. We can see here, and also here, right? So here, it has -3, and here there is also -3.

- those are factors they have in common, so they are called common factors. The terminology is not that important. We will extract -3 because both sides contains it. By making parenthesis. So the first term is - consist of this and other which were multiplied together. What was the other which was multiplied? Multiply x, right? Next, here, the second one, what do we need? +2. Yes, we need +2? +2y here. So it will be like this. So if we factorize the top, it will be like this. If we expand the bottom, we will get this. Fatorization and expansion are like friends to each other. That's right. Inseparable, complete soulmate. Rather than friends, they are enemies. Because they are opposites to each other. Like Romeo and Juliet? [*Expansion and Factorization are]. Opposing but very similar in terms of relationship. Love-hate relationship. Love-hate..relationship.

- Is this important? - Hahahahaha. - 2x^2y - 3xy^2. - The first one is a term, - including the sign, the second one is also a term. - What is their common factor? - 1. - There is 1, but usually we don't express it. - What else besides 1? - x and y?
- x and y, that's right. - So the common factors are xy.
- I got it right. - We only thought about numbers. - You need to think about the letters, too. - There are no common factors, only 1, as you said.
- Right. - There are common letters, xy. - So let's make a parenthesis and start factorizing. - How do we do it from there? - You can do it. - It must be multiplied to get this. - There is 2 here, but there's no 2 on the other one, so put 2 here. - It has 2 x's so put x.
- Correct.

- The x is doubled here, so put x here. - Wow!
- Done! - This is it, for the first term. - This is it for the first one. - Now, we must do this one. [*Let's factorize the second term.]
- Now, we must do this one. [*Let's factorize the second term.]
- This is the result of those two multiplied, right? - There is -3, so?
- Put -3. - x is both here and there, so we don't need to put it down.
- Right. - Then?
- y. - We only need to add y, right? This is it. [*Simplest Factorization completed.]
- Applause! [Let's reverse check with expansion!] - When I was young, I couldn't solve this, I just skipped it. - This is the answer to the factorization problems which appears on 9th Grade mid-term exams. - That was it.
- This is quite easy. - I think I can do it after understanding it.

- Why didn't I know him before... [Overwhelmed with joy] 
- Why didn't I know him before... - This is nothing special, right? - These must be multiplied, - to result in this term - These must be multiplied to result in this term as well [*Practicing with another equation] 
- 2x^4 - 2x^4a^2bc - 10x^3ade^2 
Please factorize the equation! - This is too easy~ - Yes, it's easy 
- We know how it works now - Yes, it's not like we must memorize it - To convert to a single term, what is the common factor that is a number? - 2 
- Yes! 2 - This is 2X5 and this is 2X1, so it should be 2 - Let's try the letters - Now, here are 4 x's - Here we have 3 x's, what would be the common factor?

- x...3.
- No, just x. This is the same problem. There are 4 chocolates next to me, and I personally have 3 chocolates. How many do we have in common? Is it a chocolate or 3 chocolates?
- A chocolate. You could say we have a chocolate in common, but extracting the highest factor would be much beneficial later.
- Then 3 chocolates. Right, so 3 chocolates. [*Extract the highest common factor]
- So here, too? x^3. Next, this has two a's and here's one a's, so? Just a. OK, just one a. Here's one, but the other has none. Is it a common factor?
- No. What about c?
- No. What about d?
- No. What about e?
- No. So this is the common factor, done. Then we extract now. Gree! x, a and dc. Continue with the next one.

-5, d and e - squared. Give him a cheer! Good job, this is called factorization. This is nothing, right? It's easy. Just changing things in terms of multiplication. Simply put, changing terms of addition and subtraction into terms of multiplication is called factorization. This class is quite fun. It's my first time learning math with cheers. Teacher... You've been living in this charming mathematics universe. It's the teacher who is charming ^^ I'm sorry, I'm joking. Darling Darling my love. [The journey to the factorization]
1. Polynomial expression
2. Expansion
3. The most basic factorization
4. More advanced expansion
5. Expansion of perfect square expression
6. Factorization of perfect square expression. [The journey to the factorization]
4. More advanced expansion. This time, we will do expansion for two equations. For example, (x+3) is what kind of equation? Linear equation.

- Then we have (2x-1). This is also a linear equation. Since they are both linear and multiplied linear twice, it becomes a quadratic equation. Linear times linear won't be linear. When multiplied linear twice, this is linear, right? This is linear too. If those are multiplied, this becomes squared. The number of multiplications indicates the kind of equation. Linear means 'multiplied once'. When multiplied linear twice, it becomes quadratic. These are both linear equations. When multiplied, it becomes quadratic. You need to know how to expand this too. Before we multiply like this as there was only one term. Now, we must multiply the first term as we did before. And then multiply the second term in the same way. So in total, there will be 4 terms. Let's try it. x times 2x, what do we get?
- 2x^2. That's right, 2x^2.

- Next, x times -1, what do we get? - -x. - So using the first term, we multiplied it to those two, right? - Now using +3 to multiply those two again, what do we get? - 6x.
- Right, 6x. - Lastly, +3 times -1 is what? - -3.
- Good work. - Looking at it, this is linear and this is also linear. - What do we get when we add those together? - 5x. - They are called 'Similar terms' as they are same kinds of terms. - This is quadratic, linear and linear. - Those are same kinds of term, so similar terms. - Similar terms can be combined together. - So as a result, you can express 2x^2 + 5x -3. - This process, people call it EXPANSION. - Reversely converting the expansion to this is called? - we call it FACTORIZATION. - So to study factorization,

- you need to know how to do the expansions. Now the main topic of the day: this might be quite difficult. Do you find it difficult, too? OMG it's so difficult, drives me crazy. What the... [EXAGGERATING]
- I can't sleep because of it. I'm scared. What we're gonna study is (a+b)^2 [The journey to the factorization].
1. Polynomial expression.
2. Expansion.
3. The most basic factorization.
4. More advanced expansion.
5. Expansion of perfect square expression.
6. Factorization of perfect square expression [The journey to the factorization].
5. Expansion of perfect square expression. This is a well-known equation. This is called PERFECT SQUARE EXPRESSION. I'm sure you know how to do this. Squared means multiplied how many times?
- twice. As multiplied twice, so in other words: (a+b) x (a+b).

- All you have to do is expand this expression, which you are good at. Multiplied those?
- a^2. This multiplication.
- ab. How about this?
- ba..ab. ab or ba is the same, right? As 2X3 = 6 and 3X2=6 is the same. So here is also ab. What about this?
- b^2. b^2, and this equation is not organized yet. We have two ab's here. If we combine these together, what do we get? 2ab.
- 2ab, correct. Finally, it becomes a^2 + 2ab + b^2. Correct?
- Yes. Is it difficult up to this point?
- No. No, right.
- Not at all. It's easy, buuuuut. Those are bad guys.
- Why? They tell to skip those process. They tell us to convert this into this right away.
- Who does?

- The bad guys.
- We must arrest them.
- We do.
- But this is required to solve quadratic equation.
- Originally, we need all those procedure to express it directly to this, just MEMORIZE.
- Memorizing it by understanding it, it's different, and just memorizing with nothing are clearly different.
- It's totally different.
- So I always tell students not to do prerequisite learning.
- Right now, most of 4th graders can solve differential and integral calculus.
- Those living in Daechi-dong [Culture Shock], they don't even know what differentiation is, but they know how to solve it? That's almost like a horror movie.
- It's child abuse in some sense.
- They have good academic scores but never score good on CSAT.
- You have a daughter, Lael who's 5th grader, the most important thing to do is, please ask her HOW THESE WORKS, everyday.
- Ask, 'how does this expansion work?'

- If you keep asking this, she will be definitely good at math. 
- If the students is around 7th graders, they wouldn't even understand - from mother's point of view. 
- In that case, think of your child IS LEARNING AS HE/SHE EXPLAINS the method. 
- If you don't understand, keep asking. 
- Then they will realized on their own. 
- They will be like 'Mom, I don't think I understand'. 
- Then, tell them to make sure to ask your teacher tomorrow. 
- This way is much, much better - this is so important [Such a useful advice...] [Jung Seungje's tips for memorizing perfect square expression expansion].
- Let's do it like this [Jung Seungje's tips for memorizing perfect square expression expansion].
- There will only be the ones with two terms. 
- Think of this as front, and think of this as back. 
- Then you only have to square the front - this, you only need to square the back.

- this middle one is the problem. How to memorize the method is to. You can see the front and back. There's 2 written here, fortunately. Just multiply all of what you can see. 2, front a and back b. Just multiply all of them which you can see, and it will be easy. [*This is only to memorize the method easily].
- although the whole explanation isn't really like this. Square of the front and back. And multiply 2, a and b. Then just write it down as it is. So look at this. If we have (a-2b)^2. The front term is a, the back term is? b.
- not exactly b. -2b. It's -2b actually. What if we square the front term? a^2. What if we square the back term?
- +4b^2. +4b^2, correct, why?

- If we square a negative number, it becomes positive. [If we multiply a negative (-) twice, we get a positive (+).] Now multiply all you can see: 2, a, and -2b. Numbers with numbers and letters with letters. So what is it for the numbers only?
- 4. With the sign?
- -4. We have a and b for the letters. You only have to do this. So those you can see, 2, a, and -2b should be multiplied together. Let's try another one. (2x-5)^2. 4x^2. Very good. The middle one?
- We will do the middle later. Oh, OK. LOL
- We will do the back first. The last one, then?
- We are used to do it like this. 25.
- +25. What about the middle? [1. the square of 2x] [2. the square of -5]
- +25

[3. 2 X 2x X (-5) in the middle]
- -20x. Right now, we are doing factorization. This falls into 9th grade course. If you understand this perfectly while in 9th grade, it will be much helpful when doing 10th grader math. Oh, really? What I recommend is, if you finish learning quadratic function until 9th grade, you wouldn't have any problem learning 10th grade math. Just do it step by step, with this attitude. Please take care of our math. Will do. As long as our math education becomes on-track, I'm ready to sacrifice myself.
- Wow. [Self-sacrifice]
- Even my music album doesn't do well. [She never gets the pitch right.]
- Darling, Darling, My love. Your melody is so wrong every time. LOL. Can you correct it for us again? Darling, Darling, My love, Beautiful my love. LOL.

- Since it's our first day, we will just do Darling My love. - OKOK LOL. [The journey to the factorization]
1. Polynomial expression.
2. Expansion.
3. The most basic factorization.
4. More advanced expansion.
5. Expansion of perfect square expression.
6. Factorization of perfect square expression. [The journey to the factorization]
6. Factorization of perfect square expression. - Let's do the proper factorization now. - This is the most difficult.
- It sounds difficult, too. - Again, for (a+b)^2. - Squaring the front,
- a^2. - Multiplying 2, a and b.
- 2ab. - Squaring the back,
- b^2. - It is called the factorization. - You must do it like this from now on. - For the front one, what makes a^2? - a must be squared, right? - So, we must put a at the front. - What was squared to get this?
- b.

- Just try to write those down. And then,
- Just do them except the middle one? Yes. And then, write down the sign of the middle as it is. If it's plus, write plus. If minus, just minus. Then, this is trial. You must check that 2 X something X something 
results the middle term or not. When you multiply 2, a and +b, do you get 2ab or not?
- We do. Then that's it. [*Try another one]
- Let's have a look at another one. When you are to factorize
x^2 - 4xy + 4y^2. This is how you do it. x^2 has been squared. 4y^2 has also been squared. This is square of what?
- 2y. Square of 2y, right? If both terms are that of squared, there is a high possibility of being perfect square expression.

- Try this. This is the square of what? X. This is the square of 2y. And take the sign from here as it is. Just check if the middle term will come out or not. Shall we? When multiplied, all 2, x, and -2y. -4xy. That's it. Then, THE END! [Validated!!] Then, THE END! So the factorization for this becomes this right here. So you said check, but is there a situation where it becomes not validated? Of course, there is. When it's not, you must use another method. Please teach us next time. Ahhhhhh. Motivated students, I love it. You just have to listen and you just know. I would like to take CSAT again, wow. Let's practice. 9x^2 - 12xy + 4 y^2. Factorize this. This and this are squared term.

[*Check if it's a perfect square expression!!!]
- In this case, - This is the square of what?
- 3x - This is the square of?
- 2y - Fantastic job - Using this connecting sign as it is - Check if it works! - It works.
- It does, right? [Validated perfect square expression!] - DONE! [Mesmerized by Maths] - Is factorization this easy?
- It's too easy. - You're doing great - When multiplied as a whole with two terms, 
generally it's a perfect square expression - This is so cool.
- Definitely cool - I think this video will be the Mecca of Mathematics [Honored].
- Mecca of Factorization - Darling Darling, My Love - That's NOT it!~! [I don't care, I love it] - Let's try one more then have a break - Now we know how to solve a quadratic equation like this.
- Isn't this too easy? - The front one is the square of?
- x.

- This is square of
- 5. Using this sign, check if it works. It does.
- BINGO. [Perfect Square expression validated]. Then this equals to 0. [*Solving for x in quadratic equation will be covered in next time!]
- After this, we haven't studied yet. The whole process of changing this is called Factorization. All good?
- Yes! Let's have a break now. Wow... [We will be continuing to master Factorization next week ^^]

[중3 수학-인수분해] 대한민국 원탑 강사 '정승제'에 홀딱 반한 홍진경(수포자필독,인수분해,eng) [공부왕찐천재]

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