Just refreshing my math, which I do every few years. This type of focused lesson is like putting oil on the old-I’m 71-mental gears. Feels smoother already.
I am 58 years old, and I have attention deficit disorder. Some advice I can give you is to GET TO THE POINT !!! Stop explaining who you are, and what you have accomplished in life. Dont describe your past students. Dont talk about excuses why the work wasn't done. I tried to comprehend your explanation of the math problem but with people like me, you only have about 5 seconds or less to keep my attention on the problem. Work the problem out, then explain why. If you start talking about something other than exactly what you're teaching, you will lose half of your class. This was a huge problem for me when I was in school, and I thought I was just dumb. Young people with this problem are afraid to talk about it. If you have students that are struggling, try talking to them. You seem like a decent person. You wont have any problem connecting.
You were not dumb, you just didn't learn the preliminary arithmetic skills which are essential for the study of algebra. The "ADD" label is simply a means to avoid responsibility for learning basic skills. The same goes for all those other feel-good labels assigned to "smart" children who won't sit down and learn. If a concept doesn't come easily and quickly, it's either because (1) the teacher is no good; (2) I've got xyz disability.
Weird part is in my country we just had to learn the 'binomic formulas' after deducting them from multiplying them out: 1st: (a +b)^2 = a^2 + 2ab + b^2 2nd: (a - b)^2 = a^2 - 2ab + b^2 3rd: a^2 - b^2 = (a + b) • (a - b) We did not make it that complicated as you expressed it. We just learnt them like vocabularies. 😉 And for you people who want to learn it: Those are really handy, even in real 'normal' life: What is 32 • 28 without a calculator? 28 • 32 = (30 + 2) • (30 - 2 ) = 900 - 4 = 896 55 • 45 = (50 + 5) • (50 - 5) = 2500 - 25 = 2475 😉 What is 32 • 32? Well... 32 • 32 = (30 + 2)^2 = 900 + 120 + 4 = 1024 That's the reason why learning quadratic numbers is so helpful.... it makes 'life at school' easier. 😉 If the numbers are not that 'nice' you can actually make REALLY good estimations in science and engineering! Let's say you need to calculate a number like 917^2 .... and now let's imagine due to very short time and urgency it does not need to be absolutely precise... just a good estimation! 😉 Using the first formula: (a +b)^2 = a^2 + 2ab + b^2 Now in this scenario if a >> b (900 >> 17).... you could say that b = 0 ... so b^2 = 0, too! 😉So 2ab = 0 as well. 😉 And so 917^2 is about 810000. The real value is 840889. The error is at about ∆ = 3,7 %! In many - but not in all! - calculations this difference is tolerable. We call it 'quick'n dirty'. For a better estimation you can use b = 20, let b^2 be 0 because a >> b and 2ab >> b^2 for b = 20 : 810000 + 36000 = 846000 (∆=0,6 %) This is pretty good already and good enough for almost all QUICK calculations aka estimations. The problem would be far worse if the error was at 1000 % or even 1.000.000.000 %.... it seems unlikely to you but this happens regularly! The difference between 102 and 100 is far smaller than the difference between 102 and 1020. In sciences we are always happy if the results of complex calculations are at least in the same region of expectated magnitude.... ( like n, µ, m, k, M, G, ...) Greetings from an M.Sc. in chemistry
I like it! Always appreciate different methods for doing math. If they taught students the value of making good estimations, it would accomplish two things-it would make it easier for the students, and it’s a good way to check your own work, to make sure you’re still in the ballpark. Or as I think of it, within reasonable range. And with some practice, you can reduce that already low error even more by squaring the first number (900), then rounding the second number to make the multiplication easier (20 instead of 17, for example) and since you know that the final estimate will be a bit larger because of the direction in which the number was rounded to, you would add or subtract a “small handful” of numbers. That takes a bit more time, but if you have the time it gets you pretty close. I don’t know if many people think of it consciously, but imagine how fortunate we are to have developed maths! Imagine the alternative. Good post-Thanks!
Where were u when I had flunked 3 years of algebra I…I finally found a class with a teacher who took his time, and gave out loads of homework! It sure helped. That’s why I tell physicists…
Wow...conjugate binomials, can’t believe that expression popped into my head after all these years (whereas I have to think to remember what I had for breakfast this morning!).
I enjoyed your post! 👊🏾 I'm 52 and that refresher course was fun! 🤓 I made it up to trigonometry in H.S., and collegiate algebra before I changed into the arts. 🎭
I'm 88 and I seem to recall that H.S. Trig was a lot different from college Trig. Well, I didn't exactly take a college course called Trig. It was called Pre-calculus which is composed of Trig and College Algebra. It might be different now, but when I took H.S. Trig there was no mention of a unit circle.
would be nice to have a cheat sheet of all the different types of factoring on it. Be good as a simple reference to jog the memory till a person doesn't need it anymore.
That's not learning, that's memorizing. It's far easier just to learn these processes so advanced concepts can be built upon a foundation of knowledge, not mindless memorization and cheat sheets.
@@rgetso I respectfully disagree. It's how a person uses the tool. Myself, I know quite a few of the factorization methods, but when I approach a problem, it would be nice to be reminded of all the rules for factorization on 1 page. My brain will fill in the details of how each type of factorization works. With enough use and practice, I won't need to refer to the cheat sheet.
@@rgetso Except the instructor SAID , very specifically, DOTS is a rule which must b known by “ROTE” or memorized. If u disagree w/ that or can prove that incorrect, why r u watching this person’s vid?
Learned this in 8th grade and still know it - I'm 63 and still know at least basic algebra - and your statement is so true.....you won't pass algebra if you don't know this. LMAO! Well said!!!
Although this is best remembered by rote, it can be graphically demonstrated. (something my teachers never did) and might be amusing for the kids. Math, amusing? Yes, way.
Aside from my work as a scientist, for which I used algebra extensively, I found many occasions to use it elsewhere. I think that, once you have several tools at your disposal, you evaluate problems and attack them using one of those tools. If algebra is one of them, you might find it quickest to use. If not, then you either find another way or avoid the problem. I actually have used this equation to calculate products in my head when the two numbers fit. Or approximate when they’re close. If you happen to have memorized the squares, for instance, that 25*25=625, then 24*26=624, 23*27=621 etc. I would never have chosen such an approach without the DOTS relationship, even though we never referred to it by the acronym. One may never be faced with such a problem, may always have a pencil and paper to work it out, or may make a calculator app on their phone. I’ve done these mental steps to solve cost estimates while driving, which kind of gets compromised by pencils or calculators.
UGH ....I'm 57 , never had to use it in life ....loved geometry and trigonometry but algebra ....UGH. I aced geometry and trig because it was interesting to me to solve problems like a puzzle but algebra didn't make sense to me . Mr. Bachman got me to a b+ because I broke up a fight between Mike B. and another student otherwise I would of gotten a C ....lol. I was an A student in everything else and I never studied ....had notes if I could find them . I used some trig in the cylinder Engraving business for diameters and radius's . It was good to reminisce for awhile seeing your video.
There's a reason why the USA is near the bottom when it comes to math and science. While this lesson is spot on right, it is a perfect example of western education. DOTS is so easy to understand when every detail is written out and explained. That was not done here in my opinion. Why? Look at the third problem in the video t^2 - 7 for example. It was explained in the /b/ term that 7 needed to be square root of 7 but it was not explained that the /a/term t^2 needed to be as well (I'm referring to writing out the radical sign - radicand#). Our teachers and instructors are no doubt brilliant, but are also the product of the same western system. Explain the math, every single step. Don't say refer to another book or chapter to catch up. This is why were being destroyed by China, Korea, India, Japan etc. Thanks for the video, it was a good refresher for me in factoring and thanks for being an educator that cares.
My friend, it is important to start with reasoning , explaining why is it so before you expect students to memorize by ‘rote’. Here it is: a simple multiplication, to show the students this step-> (a+b) x (a-b), which is in the first algebraic expression, (a+b), we take ‘a’, multiply that ‘a’ with ‘(a-b)’, then take ‘b’ in that 1st expression and multiply ‘b’ with ‘(a-b)’, Then add these two multiplied results. Doing that is as follows: a(a-b) + b(a-b) which becomes-> ‘a squared’ Minus ab + ba Minus ‘b squared’ = a sq’d minus b sq’d. Note that Minus ab + ba cancel out to zero. Not so obvious for all students beginning to learn Math unless we explain this step as reasoning and then register the factoring result as a formula to memorize. Otherwise it looks like ‘hypothesis’ , just take it, don’t ask question approach. You get it. Otherwise interesting and well presented. Thank you!
There are no numbers so you can't calculate the problem, and you haven't given me the answer. It's a whole lot of hogwash. 1+2=? that's an equation that can be calculated =3
Can't Teach An Old Dog New Tricks, they say. Well this 65yo just learned DOTS/(a+b) (a-b), which I don't recall being simplified in my intro to Algebra. Excellent video. Tks for sharing May your 2021 Christmas be filled with Joy to you and yours!
I am reviewing because I have grandkids now. They are not there yet but I KNOW their parents do not remember and will not review so when they need help with homework guess who will help. Choice one will be their Aunt who used to TEACH math at high school. Choice 2 is Grandma who lives MUCH closer.
From a young man to this day... For the majority of people , when is this ever used as a adult? . I think time spent teaching youth should be a understanding of $$ finances , debt, ect.
As a retired engineer you will never use it in your adult life. However, if you plan to go on to higher education you need it to pass higher math courses such as trigonometry, calculus, differential equations. That is if you go into the STEM field.
@@garyr4211 ua-cam.com/video/eD2hLhhYmbg/v-deo.html Millionaire Ben Hart explains Why Learn Algebra? and it is the best video on UA-cam, since you are so correct, that if a students wants to advance into higher education s/he has to have math.
Knowing how to factor the difference of squares is important, but this is useless if one doesn't know their multiplication facts well enough to realize they are looking at a difference of squares. Algebra is darn near impossible for those who never bothered to learn the multiplication table. That's also why fractions are such a mystery to them.
Yeah, and multiplication facts are useless if you don’t know your addition facts. Knowing that 2X3=2+2+2 won’t do you any good if you don’t already know what 2+2 is. Similarly, knowing that 2+2=4 is only useful if you know the meaning of +, =, and the numbers 2 and 4. Addition facts are useless if you don’t know the meanings of numbers and signs. Furthermore, knowing the meaning of 2, 4, +, and = still won’t help you in finding out what 2X3 is, if you don’t know how to count past 5. You could try explaining to someone that 2X3=6, by telling them that 2X3 is the same thing as 2+2+2, after telling them what the plus sign and the number 2 means, and telling them that the number 6 comes after the number 5, but none of that will do them a bit of good if they can’t speak English. Of course, you could say all this to them in their own native language, instead, and you could tell them how to translate their tribe’s words to English, but it will still be a big waste of time if they are at some faraway location where they can’t hear you, or if they’re listening to a loud death metal song in their native tongue while wearing headphones. Another possibility, albeit far less likely, is that they could even be deaf. Then again, instead of saying all this stuff out loud, you could just write it all down on paper, and then give it to them to read, but that will be equally useless, unfortunately, if they are also blind. The obvious solution to this situation would be to write everything in braille, but that’s not going to help them if-yep, you guessed it-they don’t have any fingers or toes. The moral of the story is that everyone is different, and in order to teach someone you have to first understand the challenges each individual faces, and then find a way to work through it. This can be very difficult, at times, for even the best of teachers. Some students will likely seem impossible to teach, and they probably will be, so there’s really no point in trying. Some people will always be dumb, no matter what you do, but that’s not actually a bad thing, at all. If it weren’t for all the people who are dumber than us, we wouldn’t have anyone to feel better than. I don’t know about you, but I sure as heck wouldn’t want to live in a world where I’m not any smarter than, and, therefore, better than, anyone else. No one wants that, I can assure you, except for, maybe, the very dumbest of people, and those doofuses certainly don’t count. They are far too dumb to know what’s good for them.
(a+b)(a-b) Factored Form. It seems weird to have set up a-squared - b-squared = ? [It's not equation; it's something to factor.] Unless you solve for a and b with square roots?
I suspect the resulted factorized formula (a + b)(a - b) may come from the conjugated pair of complex number which should be taught in upper six and seven from old British Hong Kong Advanced mathematics, am I right?
If you remember it, it may help you in an exam but other than that it has absolutely no use, in real life. I'm nearly 70,I've yet to apply this even once in my daily life.
That's the same with me and playing violin. I'm 55 and never had a use for playing the violin. However, I use elementary and somewhat advanced mathematics daily. Mathematics is a skill I developed as a child/teen and decided in my late teens that I would go pro with it. I can't say the same about violin. My violinist friend, however, uses her advanced violin skills daily to provide for her family. She's never factored a difference of squares outside of math class in school.
Think the biggest difference between UA-cam teaching and the school classroom is if content is not made intelligible to people,the channel will fail--if a poor teacher,your students won't do as well but you're unlikely to lose your job.
Is being left handed an obstacle to learning algebra ?Where my mind fails to keep up is that teachers start with a set of new definition words that my mind wants understand.What is Algebra ? How did it come to be.What does the word mean.What is algebra used for.What does factoring mean.What is the explanation of the meaning that ends with it being required Rote learning.Why can't I know that,so that I can start with a deep understanding of what I'm being asked to learn when learning algebra.
From my lifetime of experience, students, in general, are not interested in a deep understanding of mathematics or really any other academic topic. Moreover, they would not comprehend the connections and necessity of mathematics to other math-related fields. Otherwise students wouldn't continually ask, "Is this going to be on the test?" Teaching disinterested students is difficult at best. As the saying goes, "When a student is ready to learn, the teacher will appear." Oftentimes the teacher is the student. That is, we are our own best teacher. Let's not forget failure is a wonderful teacher.
I stumbled upon this video by random and thought the question "what is a^2 - b^2" looked stupid. Because it kind of is, depending on the context. "It is whatever I set it to" I thought. "It can be 1, it can be 2, or it can even be a variable x". What's missing is the context. It should be "what is a^2 - b^2 according to the rule of difference of two squares?". Also, factoring... If you can't do it, you can't do algebra. Well, learning common ways to factor equations is one thing. But try prime number factorization as a challenge. All Internet security is based on the assumption that it's a difficult problem no one can solve in reasonable time, on big enough numbers. So good like with passing algebra if you can't do it! 😆
I am not sure where "factoring" comes into play? I took algebra 1 and 2 in high school (a long time ago) and I do NOT remember ever seeing anything like this?
X2-9=x2-3/2 it doesn’t make sense to me because there is 3,3 in 9 and you only use 2 in the translation to 3/2’s and in your next problem 16y2 is now translated into 4y evenly 4x4= 16 , when 3x3 = 9 not 3x2=6 ?
I had a hard time with algebra and I was told that my instructor didn’t start with the basics of algebra. Do you agree with that? If so please explain what the basics is.
It's been 50 years, but my question is still the same. Why did you assume those particular numbers? I know that the values are relative and this is to show the process, but I used to drive my algebra teacher crazy. Lol.
@@squatch253 I can relate to your experience. I failed algebra 1 and 2 and really struggled to pass both. My school adviser, a great man , recommended geometry. I tried it and wow, I was a star. Everything suddenly clicked when I could see a practical usage.
ua-cam.com/video/eD2hLhhYmbg/v-deo.html Millionaire Ben Hart explains in this video why high school Algebra is the make or break class for students and why it is necessary for all the successful jobs. To me, it is a shame that girls are told they can't do math.
If you learn how to factor, then you don’t have to memorize anything, especially formulas, because that will lead to mistakes that you can’t identify or understand. Learn the basis of the formula, not the formulas!
Bro I am sure you are good however you need to come to the point directly and not go round and round about it because it actually confuses one’s mind. Please take it as a constructive advice.
Just refreshing my math, which I do every few years. This type of focused lesson is like putting oil on the old-I’m 71-mental gears. Feels smoother already.
Agreed. We Polish folk like to keep the gears oiled as we get older. Good man.
I'm 66 and totally understand.
I had a college professor teach me algebra. The way she taught me, I could do them in my head! Too bad I have forgotten all of it.
I am 58 years old, and I have attention deficit disorder. Some advice I can give you is to GET TO THE POINT !!! Stop explaining who you are, and what you have accomplished in life. Dont describe your past students. Dont talk about excuses why the work wasn't done. I tried to comprehend your explanation of the math problem but with people like me, you only have about 5 seconds or less to keep my attention on the problem. Work the problem out, then explain why. If you start talking about something other than exactly what you're teaching, you will lose half of your class. This was a huge problem for me when I was in school, and I thought I was just dumb. Young people with this problem are afraid to talk about it. If you have students that are struggling, try talking to them. You seem like a decent person. You wont have any problem connecting.
algebra sux no simple about it
You were not dumb, you just didn't learn the preliminary arithmetic skills which are essential for the study of algebra. The "ADD" label is simply a means to avoid responsibility for learning basic skills. The same goes for all those other feel-good labels assigned to "smart" children who won't sit down and learn. If a concept doesn't come easily and quickly, it's either because (1) the teacher is no good; (2) I've got xyz disability.
@@rgetso you missed out on learning diplomacy skills
He's very easy to understand you need to relax and learn
Hell yeah!!!!
Weird part is in my country we just had to learn the 'binomic formulas' after deducting them from multiplying them out:
1st: (a +b)^2 = a^2 + 2ab + b^2
2nd: (a - b)^2 = a^2 - 2ab + b^2
3rd: a^2 - b^2 = (a + b) • (a - b)
We did not make it that complicated as you expressed it. We just learnt them like vocabularies. 😉
And for you people who want to learn it:
Those are really handy, even in real 'normal' life: What is 32 • 28 without a calculator?
28 • 32 = (30 + 2) • (30 - 2 ) = 900 - 4 = 896
55 • 45 = (50 + 5) • (50 - 5) = 2500 - 25 = 2475 😉
What is 32 • 32? Well... 32 • 32 = (30 + 2)^2 = 900 + 120 + 4 = 1024
That's the reason why learning quadratic numbers is so helpful.... it makes 'life at school' easier. 😉
If the numbers are not that 'nice' you can actually make REALLY good estimations in science and engineering!
Let's say you need to calculate a number like 917^2 .... and now let's imagine due to very short time and urgency it does not need to be absolutely precise... just a good estimation! 😉
Using the first formula: (a +b)^2 = a^2 + 2ab + b^2
Now in this scenario if a >> b (900 >> 17).... you could say that b = 0 ... so b^2 = 0, too! 😉So 2ab = 0 as well. 😉
And so 917^2 is about 810000. The real value is 840889. The error is at about ∆ = 3,7 %! In many - but not in all! - calculations this difference is tolerable. We call it 'quick'n dirty'.
For a better estimation you can use b = 20, let b^2 be 0 because a >> b and 2ab >> b^2
for b = 20 :
810000 + 36000 = 846000 (∆=0,6 %)
This is pretty good already and good enough for almost all QUICK calculations aka estimations.
The problem would be far worse if the error was at 1000 % or even 1.000.000.000 %.... it seems unlikely to you but this happens regularly! The difference between 102 and 100 is far smaller than the difference between 102 and 1020. In sciences we are always happy if the results of complex calculations are at least in the same region of expectated magnitude.... ( like n, µ, m, k, M, G, ...)
Greetings from an M.Sc. in chemistry
I like it! Always appreciate different methods for doing math. If they taught students the value of making good estimations, it would accomplish two things-it would make it easier for the students, and it’s a good way to check your own work, to make sure you’re still in the ballpark. Or as I think of it, within reasonable range. And with some practice, you can reduce that already low error even more by squaring the first number (900), then rounding the second number to make the multiplication easier (20 instead of 17, for example) and since you know that the final estimate will be a bit larger because of the direction in which the number was rounded to, you would add or subtract a “small handful” of numbers. That takes a bit more time, but if you have the time it gets you pretty close.
I don’t know if many people think of it consciously, but imagine how fortunate we are to have developed maths! Imagine the alternative.
Good post-Thanks!
Where were u when I had flunked 3 years of algebra I…I finally found a class with a teacher who took his time, and gave out loads of homework! It sure helped. That’s why I tell physicists…
Excellent presentation! Thank you! 😊
It's called the difference of two squares. a^2-b^2=(a+b)(a-b)
Wow...conjugate binomials, can’t believe that expression popped into my head after all these years (whereas I have to think to remember what I had for breakfast this morning!).
I enjoyed your post! 👊🏾 I'm 52 and that refresher course was fun! 🤓 I made it up to trigonometry in H.S., and collegiate algebra before I changed into the arts. 🎭
I'm 88 and I seem to recall that H.S. Trig was a lot different from college Trig. Well, I didn't exactly take a college course called Trig. It was called Pre-calculus which is composed of Trig and College Algebra. It might be different now, but when I took H.S. Trig there was no mention of a unit circle.
would be nice to have a cheat sheet of all the different types of factoring on it. Be good as a simple reference to jog the memory till a person doesn't need it anymore.
That's not learning, that's memorizing. It's far easier just to learn these processes so advanced concepts can be built upon a foundation of knowledge, not mindless memorization and cheat sheets.
@@rgetso I respectfully disagree. It's how a person uses the tool. Myself, I know quite a few of the factorization methods, but when I approach a problem, it would be nice to be reminded of all the rules for factorization on 1 page. My brain will fill in the details of how each type of factorization works. With enough use and practice, I won't need to refer to the cheat sheet.
@@rgetso Except the instructor SAID , very specifically, DOTS is a rule which must b known by “ROTE” or memorized. If u disagree w/ that or can prove that incorrect, why r u watching this person’s vid?
Learned this in 8th grade and still know it - I'm 63 and still know at least basic algebra - and your statement is so true.....you won't pass algebra if you don't know this. LMAO! Well said!!!
Although this is best remembered by rote, it can be graphically demonstrated. (something my teachers never did) and might be amusing for the kids. Math, amusing? Yes, way.
3 kinds of people understand math, those that do, and those that don’t.
And those that can't count.
@@samtheshame9951 It was an old joke,
@@vonrock6862 and that was a joke, he said 3 kinds and only named 2
@@samtheshame9951 well, you see if he understood math he would of said 2, that’s the joke, maybe over your genius.
@@vonrock6862I knew the joke
I am 62 years old and not one time during my lifetime was I confronted with a situation that required Algebra
58 here and the same, never needed it ever
Aside from my work as a scientist, for which I used algebra extensively, I found many occasions to use it elsewhere. I think that, once you have several tools at your disposal, you evaluate problems and attack them using one of those tools. If algebra is one of them, you might find it quickest to use. If not, then you either find another way or avoid the problem. I actually have used this equation to calculate products in my head when the two numbers fit. Or approximate when they’re close. If you happen to have memorized the squares, for instance, that 25*25=625, then 24*26=624, 23*27=621 etc. I would never have chosen such an approach without the DOTS relationship, even though we never referred to it by the acronym. One may never be faced with such a problem, may always have a pencil and paper to work it out, or may make a calculator app on their phone. I’ve done these mental steps to solve cost estimates while driving, which kind of gets compromised by pencils or calculators.
OMG I paused it doing 16y-25= and with your cursor was a dot and in-between the 2 an5 lol drove me nuts thinking sq of 2.5. Either way great video.
UGH ....I'm 57 , never had to use it in life ....loved geometry and trigonometry but algebra ....UGH. I aced geometry and trig because it was interesting to me to solve problems like a puzzle but algebra didn't make sense to me . Mr. Bachman got me to a b+ because I broke up a fight between Mike B. and another student otherwise I would of gotten a C ....lol. I was an A student in everything else and I never studied ....had notes if I could find them . I used some trig in the cylinder Engraving business for diameters and radius's . It was good to reminisce for awhile seeing your video.
Sad to say those who have difficulty in math or algebra does not know the laws if exponent and factoring. This is used up to advance mathematics.
There's a reason why the USA is near the bottom when it comes to math and science. While this lesson is spot on right, it is a perfect example of western education. DOTS is so easy to understand when every detail is written out and explained. That was not done here in my opinion. Why? Look at the third problem in the video t^2 - 7 for example. It was explained in the /b/ term that 7 needed to be square root of 7 but it was not explained that the /a/term t^2 needed to be as well (I'm referring to writing out the radical sign - radicand#). Our teachers and instructors are no doubt brilliant, but are also the product of the same western system. Explain the math, every single step. Don't say refer to another book or chapter to catch up. This is why were being destroyed by China, Korea, India, Japan etc. Thanks for the video, it was a good refresher for me in factoring and thanks for being an educator that cares.
My friend, it is important to start with reasoning , explaining why is it so before you expect students to memorize by ‘rote’. Here it is: a simple multiplication, to show the students this step-> (a+b) x (a-b), which is in the first algebraic expression, (a+b), we take ‘a’, multiply that ‘a’ with ‘(a-b)’, then take ‘b’ in that 1st expression and multiply ‘b’ with ‘(a-b)’, Then add these two multiplied results. Doing that is as follows: a(a-b) + b(a-b) which becomes-> ‘a squared’ Minus ab + ba Minus ‘b squared’ = a sq’d minus b sq’d. Note that Minus ab + ba cancel out to zero.
Not so obvious for all students beginning to learn Math unless we explain this step as reasoning and then register the factoring result as a formula to memorize. Otherwise it looks like ‘hypothesis’ , just take it, don’t ask question approach. You get it. Otherwise interesting and well presented. Thank you!
There are no numbers so you can't calculate the problem, and you haven't given me the answer. It's a whole lot of hogwash. 1+2=? that's an equation that can be calculated =3
Can't Teach An Old Dog New Tricks, they say.
Well this 65yo just learned DOTS/(a+b) (a-b), which I don't recall being simplified in my intro to Algebra.
Excellent video. Tks for sharing
May your 2021 Christmas be filled with Joy to you and yours!
Thank you!
I am reviewing because I have grandkids now. They are not there yet but I KNOW their parents do not remember and will not review so when they need help with homework guess who will help. Choice one will be their Aunt who used to TEACH math at high school. Choice 2 is Grandma who lives MUCH closer.
The Pathagoras therum. One of the most used algebraic equations of my career.
From a young man to this day... For the majority of people , when is this ever used as a adult? . I think time spent teaching youth should be a understanding of $$ finances , debt, ect.
As a retired engineer you will never use it in your adult life. However, if you plan to go on to higher education you need it to pass higher math courses such as trigonometry, calculus, differential equations. That is if you go into the STEM field.
@@garyr4211 ua-cam.com/video/eD2hLhhYmbg/v-deo.html Millionaire Ben Hart explains Why Learn Algebra? and it is the best video on UA-cam, since you are so correct, that if a students wants to advance into higher education s/he has to have math.
Very Helpful.
Many thanks.
Greetings. (a^2 -b^2) = (a-b)(a +b)
because (a-b)(a+b) = a^2 +ab-ab-b^2 = a^2-b^2 = the original expression.
Knowing how to factor the difference of squares is important, but this is useless if one doesn't know their multiplication facts well enough to realize they are looking at a difference of squares. Algebra is darn near impossible for those who never bothered to learn the multiplication table. That's also why fractions are such a mystery to them.
Yeah, and multiplication facts are useless if you don’t know your addition facts. Knowing that 2X3=2+2+2 won’t do you any good if you don’t already know what 2+2 is.
Similarly, knowing that 2+2=4 is only useful if you know the meaning of +, =, and the numbers 2 and 4. Addition facts are useless if you don’t know the meanings of numbers and signs.
Furthermore, knowing the meaning of 2, 4, +, and = still won’t help you in finding out what 2X3 is, if you don’t know how to count past 5.
You could try explaining to someone that 2X3=6, by telling them that 2X3 is the same thing as 2+2+2, after telling them what the plus sign and the number 2 means, and telling them that the number 6 comes after the number 5, but none of that will do them a bit of good if they can’t speak English.
Of course, you could say all this to them in their own native language, instead, and you could tell them how to translate their tribe’s words to English, but it will still be a big waste of time if they are at some faraway location where they can’t hear you, or if they’re listening to a loud death metal song in their native tongue while wearing headphones. Another possibility, albeit far less likely, is that they could even be deaf.
Then again, instead of saying all this stuff out loud, you could just write it all down on paper, and then give it to them to read, but that will be equally useless, unfortunately, if they are also blind.
The obvious solution to this situation would be to write everything in braille, but that’s not going to help them if-yep, you guessed it-they don’t have any fingers or toes.
The moral of the story is that everyone is different, and in order to teach someone you have to first understand the challenges each individual faces, and then find a way to work through it. This can be very difficult, at times, for even the best of teachers.
Some students will likely seem impossible to teach, and they probably will be, so there’s really no point in trying. Some people will always be dumb, no matter what you do, but that’s not actually a bad thing, at all. If it weren’t for all the people who are dumber than us, we wouldn’t have anyone to feel better than.
I don’t know about you, but I sure as heck wouldn’t want to live in a world where I’m not any smarter than, and, therefore, better than, anyone else. No one wants that, I can assure you, except for, maybe, the very dumbest of people, and those doofuses certainly don’t count. They are far too dumb to know what’s good for them.
@@chriswebster24: Wow! What a lengthy response. Seems like a short story book - lol
(a-b)(a+b)= a^2-b^2
Thank you sir .. please help me pass my Ged math . Need it to get my tasc diploma.
(a-b)(a+b)
(a+b)(a-b) Factored Form.
It seems weird to have set up a-squared - b-squared = ? [It's not equation; it's something to factor.]
Unless you solve for a and b with square roots?
a^2-b^2
(a+b)(a-b)
Could never do Maths at school! It just never made sense to me. Must have been a future humanities Student!
Thank you..
I suspect the resulted factorized formula (a + b)(a - b) may come from the conjugated pair of complex number which should be taught in upper six and seven from old British Hong Kong Advanced mathematics, am I right?
Very helpful
If you remember it, it may help you in an exam but other than that it has absolutely no use, in real life. I'm nearly 70,I've yet to apply this even once in my daily life.
That's the same with me and playing violin. I'm 55 and never had a use for playing the violin. However, I use elementary and somewhat advanced mathematics daily. Mathematics is a skill I developed as a child/teen and decided in my late teens that I would go pro with it. I can't say the same about violin. My violinist friend, however, uses her advanced violin skills daily to provide for her family. She's never factored a difference of squares outside of math class in school.
Thanks for 1he headache,
I`m now 57 and passed algebra at school but not once in 41 years have I used algebra
5 squared -4 squared = 3 squared and multiples like 10 8 6 15 12 and 9 and so on
Think the biggest difference between UA-cam teaching and the school classroom is if content is not made intelligible to people,the channel will fail--if a poor teacher,your students won't do as well but you're unlikely to lose your job.
Answer. (a+b)×(a-b)
= (a+b)(a-b)
X^2-9
(x+3)(x-3)
Is being left handed an obstacle to learning algebra ?Where my mind fails to keep up is that teachers start with a set of new definition words that my mind wants understand.What is Algebra ? How did it come to be.What does the word mean.What is algebra used for.What does factoring mean.What is the explanation of the meaning that ends with it being required Rote learning.Why can't I know that,so that I can start with a deep understanding of what I'm being asked to learn when learning algebra.
From my lifetime of experience, students, in general, are not interested in a deep understanding of mathematics or really any other academic topic. Moreover, they would not comprehend the connections and necessity of mathematics to other math-related fields. Otherwise students wouldn't continually ask, "Is this going to be on the test?" Teaching disinterested students is difficult at best.
As the saying goes, "When a student is ready to learn, the teacher will appear." Oftentimes the teacher is the student. That is, we are our own best teacher. Let's not forget failure is a wonderful teacher.
I stumbled upon this video by random and thought the question "what is a^2 - b^2" looked stupid. Because it kind of is, depending on the context. "It is whatever I set it to" I thought. "It can be 1, it can be 2, or it can even be a variable x".
What's missing is the context. It should be "what is a^2 - b^2 according to the rule of difference of two squares?".
Also, factoring... If you can't do it, you can't do algebra. Well, learning common ways to factor equations is one thing. But try prime number factorization as a challenge. All Internet security is based on the assumption that it's a difficult problem no one can solve in reasonable time, on big enough numbers. So good like with passing algebra if you can't do it! 😆
I am not sure where "factoring" comes into play? I took algebra 1 and 2 in high school (a long time ago) and I do NOT remember ever seeing anything like this?
a^2 - b^2 = c^2
Terrific
Should (3h+1) (-h+1) multiply out to give the original (h+1)^2- 4h^2….? I can't get it to equal...
Any ideas?
.... = -3h^2 + 2h + 1
I don't think root2 is anything to do with your expression.
X2-9=x2-3/2 it doesn’t make sense to me because there is 3,3 in 9 and you only use 2 in the translation to 3/2’s and in your next problem 16y2 is now translated into 4y evenly 4x4= 16 , when 3x3 = 9 not 3x2=6 ?
(a+b)(a-b) .... trivial
A"2 - B'2 =A'2 - B'2. The point of factoring is what I need to Know
EZ
A^2 - B^2 = (a-b) (a+b)
we learn it sooner than u guy :V
Ooh! OOH! I remember now! a^2 - b^2 =(a+b)(a-b)
Students can't even make change at the cash register or make out an envelope to mail, try teaching some basics to students first.
(a+b)(a-b)= 0
algebra for beginners?
How about a² + b² = ?
@Lunga Dudumashe try
(a + ib)*(a - ib), where i is the imaginary operator defined by i² = -1.
I appreciated the comment of homer 5802 to cut short of yourself.
the preface is too long!
The problem with that class is that you neglected to show the students a practical application where the would see it in real life.
I had a hard time with algebra and I was told that my instructor didn’t start with the basics of algebra. Do you agree with that? If so please explain what the basics is.
I had it but you lost me at "17:43".
#factoring #factor #binomial #polynomial
Did it in 10 seconds. No pen, no paper.
I find no value for any “letters”.
You lost me with a+b squared. how did you come to that conclusion. to me it looks like a+b multiplied by a-b cancel each other out.
Algebra bites. I don't need it. It gave me headaches all thru college. Have I used it since? Nope!
this is Bs who said a2-b2 is equal to a+b (a-b) answer no one
It's been 50 years, but my question is still the same. Why did you assume those particular numbers? I know that the values are relative and this is to show the process, but I used to drive my algebra teacher crazy. Lol.
I’ve always had trouble with abstract concepts like algebra. I mean, all these a’s and b’s don’t really mean anything.
@@squatch253 I can relate to your experience. I failed algebra 1 and 2 and really struggled to pass both. My school adviser, a great man , recommended geometry. I tried it and wow, I was a star. Everything suddenly clicked when I could see a practical usage.
I'm sorry, would you mind repeating that? lol
👍👍
I don't like using letters in math. Just numbers
Algebra ........ the Astrology of Mathematics.
I have never had a reason to use algebra in my life and I'm in my 60's . The majority people don't need it in their daily lives.
ua-cam.com/video/eD2hLhhYmbg/v-deo.html Millionaire Ben Hart explains in this video why high school Algebra is the make or break class for students and why it is necessary for all the successful jobs. To me, it is a shame that girls are told they can't do math.
if you were my Math teacher, I could have been now a scientist or a doctor
Rachel Maddow is no match for you. She repeats EVERYTHING at least three times during a six minute spot that should be one minute. You have her beat.
If you learn how to factor, then you don’t have to memorize anything, especially formulas, because that will lead to mistakes that you can’t identify or understand. Learn the basis of the formula, not the formulas!
I don’t know. I was too busy kissing all the girls.
if it takes 16 mins\utes to teach this then someone else needs some help
Bro I am sure you are good however you need to come to the point directly and not go round and round about it because it actually confuses one’s mind. Please take it as a constructive advice.
This is for 7th grade math so, please think before you say something
Your talking to much....just show how to do the problem
Stop babbling, get to point.
It took 10 minutes to get to the formula. It’s a waste of time. You talk too much.
When I was in high school in 1958 they used this same BS. Nothing has changed. Try to teach something with no context.
Too much chatter.
Who cares?
way too long winded
Video is WWAYYYYY too long.
You don’t impress me. You may know but you can’t relate. Thumbs down.
Too much irrelevant bs. Just the facts please
I hate math 🤣
Another example of a teacher who thinks that everything is understood once he said it …
Poor pedagogic skills.
Excellent narcissistic skills.
Full of crap
(a+b)(a-b)
(A+b)(a-b)
(a+b)(a-b)