factoring trinomials with "a" greater than 1

Поделиться
HTML-код
  • Опубликовано: 27 янв 2025

Комментарии • 1,5 тыс.

  • @brasil10pedro10
    @brasil10pedro10 8 лет назад +379

    Learned more in 8 minutes than in 53 minutes of class. Thank you so much Not all hero"s wear capes.

  • @lanachesley6965
    @lanachesley6965 9 лет назад +651

    I was sick the day in 8th grade when my math class learned this, and for the next five years I never completely understood how to factor polynomials when "a" was not 1, and for the first time since 8th grade (I'm in college now, somehow) I finally understand. I can't thank you enough for this.

    • @zachlemay88
      @zachlemay88 9 лет назад +17

      Ha, When my class learned this it was a vaccination day so I never learned it fully, 4 months later here I am losing marks for this topic, thank god for this video!

    • @ComputerTechnic217
      @ComputerTechnic217 7 лет назад +4

      why did you class come to school during vacation day little boy

    • @rakeman1396
      @rakeman1396 7 лет назад +8

      Rifath vaccination day m8

    • @sofiawei352
      @sofiawei352 6 лет назад +5

      that's exactly what happened to me in fourth grade, so now idk how to do long division.

    • @jinseulpark5618
      @jinseulpark5618 6 лет назад

      Lana Chesley wew haha

  • @kennab6169
    @kennab6169 8 лет назад +173

    Ma'am you are an absolute life saver. I understood this better here than I did in class. I appreciate you taking the time to do this.

  • @misskayleebugs
    @misskayleebugs 7 лет назад +812

    Did anyone else bust out laughing when she popped up from the corner and said "hello!"

  • @Angela-pq2iw
    @Angela-pq2iw 8 лет назад +212

    I have math test tomorrow. Ur a life saver thanks!!

  • @harrypatel7805
    @harrypatel7805 7 лет назад +886

    Why is she not a meme

    • @morthslogisticsllc3473
      @morthslogisticsllc3473 5 лет назад +6

      What is a meme

    • @adilkapskapadia2662
      @adilkapskapadia2662 5 лет назад +97

      @@morthslogisticsllc3473 it's a mathematical expression only geniuses can understand.

    • @richan288
      @richan288 5 лет назад +6

      @@adilkapskapadia2662 wow ur a genius

    • @harutokato3922
      @harutokato3922 5 лет назад +3

      @@richan288 yeh because we understand that mathematically XD

    • @alexanderkyprianou3886
      @alexanderkyprianou3886 5 лет назад +22

      she looks like shes about to ask for the manager lmao

  • @jackshotthat
    @jackshotthat 2 года назад +16

    After 10 years, this video still helping people!

    • @saatvikjha4035
      @saatvikjha4035 2 года назад +2

      Yeah dude

    • @RebeccaSavell
      @RebeccaSavell  2 года назад +5

      Yay!

    • @t.n.h.ptheneohumanpatterna8334
      @t.n.h.ptheneohumanpatterna8334 Год назад

      @@RebeccaSavell can you pls be more specific u didn’t explain what if there wasn’t any common number like a number like 5 and 2 and now I’m stuck cause I don’t know what to do if a nub,ef doesn’t go into both 5 and 2 pls be more specific

    • @mustafamustafae5715
      @mustafamustafae5715 Год назад

      Yeh lels

  • @kaistahly3260
    @kaistahly3260 5 лет назад +365

    stop reading the comments you have a test tomorrow!

  • @theistnate
    @theistnate Год назад +12

    13 years later and she's still saving all our grades

  • @csqiggl2311
    @csqiggl2311 4 года назад +3

    i have online school now from corona and honestly this old old vid is the only thing that helped me understand this out of hundreds of videos and hours of searching i cant thank u enough

  • @kura-kuni9
    @kura-kuni9 Год назад +6

    you make everything so much more clear in just a 7 min video while my math teacher throws stuff at us and expects us to understand on our own and can’t even bother to make sure we understand thank you so much 😭 ❤

  • @stardude54321
    @stardude54321 8 лет назад +638

    please replace my current math teacher lol

  • @ajpoloney
    @ajpoloney 3 года назад +3

    Is this anybody else’s comfort video anytime they come across factoring? I can’t even tell you how many times I’ve watched it and it helps every time

    • @RebeccaSavell
      @RebeccaSavell  2 года назад

      Oh! Thanks! I'm a comfort channel! ;)

  • @zxhrx.n
    @zxhrx.n 8 лет назад +155

    WHEN SHE ADDS 'ISNT THAT EASY' AT THE END

  • @avery9239
    @avery9239 11 месяцев назад +7

    14 years later and she’s helping me out with alg.2

    • @RebeccaSavell
      @RebeccaSavell  10 месяцев назад +1

      I'm glad to be a help for you!

  • @mjlucanas
    @mjlucanas 5 лет назад +32

    Woman: pops out from the bottom "hello!"
    Me: "hello"

  • @lorilyntenney7691
    @lorilyntenney7691 10 лет назад +102

    Thank you for taking the time to simply ask, "What common factor do we have in both the 10 and the 15?" Why doesn't my textbook tell me that's where factoring out starts for the second grouping? I really wish I had found you hours ago! I won't lose your channel now though! :) Thanks again!

    • @RebeccaSavell
      @RebeccaSavell  10 лет назад +24

      You are quite welcome. I'm glad it helped.

    • @drabberfrog
      @drabberfrog 5 лет назад +1

      @@RebeccaSavell thanks for the help with math homework

    • @MsChinchy101
      @MsChinchy101 4 года назад +1

      Exactly! I wish I could get her as a tutor

  • @user-lg1ik9gw5x
    @user-lg1ik9gw5x 5 лет назад +4

    Out if all the people on RUclips that tried to show me how to do this equation you explained it the best and most thoroughly, thank you so much!

  • @senosuccess6412
    @senosuccess6412 Год назад +4

    I've never had a simple method to factoring a trinomial like this. Thank you! you're a great teacher.

  • @fishguru-
    @fishguru- 9 лет назад +56

    this vid helped more than any other vid i saw about quad trinomials

    • @esszee455
      @esszee455 9 лет назад +4

      +Devin Reed what is "quad trinominal"?

    • @MafiaXenaFedora
      @MafiaXenaFedora 9 лет назад

      +Awais Naseem I think he might mean the group factors?

    • @ryangoods7949
      @ryangoods7949 9 лет назад +1

      +Awais Naseem Quadratic Trinomial. Quadratic takes the form ax^2 + bx + c and a trinomial means it has 3 terms a,b,c. A Binomial Quad would be something like x^2 - 25.

    • @kurtvelasco7369
      @kurtvelasco7369 7 лет назад

      Devin
      Mim

  • @saucyragu
    @saucyragu 7 лет назад +25

    Her: “You only need math skills”
    Me: “welp time to wrap it up here, gotta go”

  • @prophetofgarfield
    @prophetofgarfield 4 года назад +1

    i have been looking for a video about factoring trinomials for the last three days and finally i understand this. thank you

  • @kaidenhills1820
    @kaidenhills1820 6 лет назад +18

    "This should look suspiciously familiar" when she said this I broke out laughing

  • @deathsheadmothranch7188
    @deathsheadmothranch7188 3 года назад +3

    This video has saved my educational life many many times. It’s my go to video when I need help for factoring, because I tend to forget the steps a lot

  • @FrankCordovaMileHighBorn
    @FrankCordovaMileHighBorn 3 года назад +7

    Whoa, I learned a lot more of factoring from you than when I was in grade school. Guys, factoring is a math skill, and a great one to have.

  • @keithdawes2685
    @keithdawes2685 11 лет назад

    Excellent. You factored out all unnecessary and confusing words resulting in a clear and concise explanation. Thank you

  • @andrearoyal2399
    @andrearoyal2399 2 года назад +4

    Was really struggling until I watched this I can now complete my assignment. Your explanation is very good 👍. Thank you

  • @cutzieklutzie
    @cutzieklutzie 12 лет назад

    im in pre-calc and all of my teachers thus far have taught this kind of factoring differently. i have never seen this method but it is by far the most clear and concise version, thank you so much.

  • @JannyMaha
    @JannyMaha 2 года назад +4

    Thank you. Thank you. Thank you. I have been trying to remember how to factor polynomials when _a is greater than 1_ to teach my homeschooled child. It finally clicked. I can't thank you enough.

  • @ctb1977
    @ctb1977 5 лет назад

    I like your teaching style of "less is more". You don't over explain or use lots of words, you just quickly and simply explain in a logical fashion. Keep it simple! Thank you

  • @gabehunt1125
    @gabehunt1125 2 года назад +3

    You should upload more if you’re still into this! I love the way you taught this. I was very nervous about factoring trinomials, but you made it a lot easier for me.

    • @RebeccaSavell
      @RebeccaSavell  2 года назад

      Thanks, Gabe. I actually have some time this summer. I plan to ask subscribers about their math needs. What do you need in terms of math concept help?

  • @okkind408
    @okkind408 5 лет назад +1

    I learned more in less than 8 minutes comparing to a hour of teaching in class. Thank you so much you are a life saver.

  • @tashiki8641
    @tashiki8641 Год назад +3

    I'm amazed that a 13year old video is helping me understand this lesson more than those recently uploaded videos.

    • @RebeccaSavell
      @RebeccaSavell  Год назад

      I'm SO glad it helped you! Thanks for watching!

  • @8LilliFlower8
    @8LilliFlower8 11 лет назад

    Finally no shortcuts. Love it when each step is explained and shown. Just went through a trillion videos and this was the ONE I could understand.

  • @ryleegaly8679
    @ryleegaly8679 4 года назад +4

    Thank you, this was so helpful. For some reason we did not cover what to do when the leading coefficient was not 1 in lecture, and it did not "click" until I watched this.

  • @nutkin6145
    @nutkin6145 5 лет назад

    You are the first source I found who taught this method using an equation that WASN'T super easy to solve. Thanks!

  • @GWiz415
    @GWiz415 9 лет назад +10

    You have the best example. Iv'e done a lot of research on finding ways to complete this and this is perfect, thank you.

  • @TophBlue
    @TophBlue 12 лет назад

    Not a single teacher I have been taught math to has ever explained trinomials in this way, and yet this method is the easiest I have ever understood. Excellent explanation!

  • @kaylagamez5539
    @kaylagamez5539 9 лет назад +79

    BLESS THIS VIDEO AND YOU

    • @_A_343
      @_A_343 6 лет назад +2

      Bless you too beautiful.

  • @76disproportionatelemurs
    @76disproportionatelemurs 2 года назад +1

    One of the best videos I could find. Everything was fully explained. It is amazing to me how math teachers can skip entire steps because they assume every student in the class knows perfectly well how to do every step. As a teacher, the opposite should be true. You should assume they do not, and explain every step, at least when introducing new topics, especially complex ones like factoring trinomials with numbers greater than one out front.

  • @jinniejinjin5290
    @jinniejinjin5290 5 лет назад +3

    You are my savior, I was so mad at myself that I couldn’t remember this and you helped me remember how to do it

  • @deanmachine9486
    @deanmachine9486 7 лет назад

    I’ve was sick at home for two days of this lesson and now I know it better than most of the class. Thank you very much!

  • @navysailor1980
    @navysailor1980 Год назад +4

    I have seen a lot of videos on the factoring topic but most of them lack explanation, but your video is above all those other videos. Thank you for the clear explanation. A lot of people just race through problems on youtube without explaining much at all, and I had the same problem in HS. The math teacher we had was a arrogant asshole and I learned a lot about him, and how emotional he was and his ways, but not Algebra.

    • @RebeccaSavell
      @RebeccaSavell  7 месяцев назад

      Thank you. I'm glad it helped!

  • @bribarlim
    @bribarlim 7 лет назад

    I'm graduating college in a week and I've always had trouble with factoring trinomials until I saw your video. You're a saint.

  • @MWWM-jw5mm
    @MWWM-jw5mm 2 года назад +3

    Oh my gosh, I'm Korean. Actually my English listening is not good. Even though I don't understand what she is saying in English exactly, she has made me understand how to solve this problem by only watching this video!
    Thank you so much!

    • @RebeccaSavell
      @RebeccaSavell  2 года назад +2

      I'm so glad you've been helped!!!!!!!!! Thanks for leaving a comment!

    • @MWWM-jw5mm
      @MWWM-jw5mm 2 года назад

      @@RebeccaSavell I have a question! Could you tell me how to solve "9s^2-16"?
      It looks different from this "6s^2-7s-3"
      I solved it like this way
      a=6, b=-7, c=-3, a*c=-18, b=(2-9)
      =6s^2+(2s-9s)-3
      =(6s^2+2s)+(-9s-3)
      =2s(3s+1) -3(3s+1)
      =(2s-3)(3s+1)

    • @MWWM-jw5mm
      @MWWM-jw5mm 2 года назад

      Oops, I think I can solve it by myself!
      I think the answer ,"9s^2-16", is (3s+4)(3s-4)!

    • @RebeccaSavell
      @RebeccaSavell  2 года назад +1

      @@MWWM-jw5mm That's correct. It's called "Factoring the difference of squares". The pattern is of you're given (a^2 - b^2), then it's factored to (a + b)(a - b).

  • @koldblaze6610
    @koldblaze6610 5 лет назад

    YOU. REBECCA SAVELL. YOU ARE AMAZING.
    I was taught 6 different methods for this and still had no clue what I was doing but THIS, this is so simple! I can't thank you enough!

  • @bullterry14
    @bullterry14 11 лет назад +12

    wow you were a light at the end of my dark algebra 2 homework tunnel!! thank you so much for your great explanation I wish you were my teacher!! lucky are your students..

  • @deelighted
    @deelighted 5 лет назад

    This is such a beautifully explained video. Why aren't more math teachers this thorough? Thank you!

  • @godsgirlmeri8573
    @godsgirlmeri8573 8 лет назад +17

    After countless hours of searching for help on factoring, this one is one I understand. Thank you so very much for this. I wonder if you have one for if there is a minus sign. Wow, how this helps me so much.

    • @ravina7716
      @ravina7716 6 лет назад

      Do you know what to do if theres a minus

    • @kod3619
      @kod3619 6 лет назад +2

      For example, if there is a negative number as c and a positive as b, then when you factor the numbers, the numbers that would match would be like, -1 + 5, and that would be a positive number. (4).

    • @mohamadkhouli9607
      @mohamadkhouli9607 4 года назад

      those hours were wasted

  • @trivarezphillip8709
    @trivarezphillip8709 8 лет назад

    Sigh, you don't know how helpful this was. Out of all the ways I've tried to do factorization of trinomials, your method was the only one that stuck with me, thanks a lot ! I subscribed, would love if you keep making more How to tutorials

  • @bernardbrachet5375
    @bernardbrachet5375 3 года назад +3

    c'est la meilleure démonstration que j'ai pu voir à ce jour !bravo

  • @taylormayzes6317
    @taylormayzes6317 6 лет назад +1

    you saved me for my GCSEs!! my teacher never taught me this, so it was amazing to see it laid out simply and easily :)

  • @stiggerloid4380
    @stiggerloid4380 4 года назад +3

    THANK YOU SOOOOO MUCH. THIS QUARANTINE IS RUINING MY LIFE!! FACTORING MAKES ME HAVE SUCH ANXIETY.

  • @Nastyc57
    @Nastyc57 7 лет назад

    This has been said more than once already but I'll say it again. Thank you. Because of you I learned in 8 minutes what my teacher could never quite explain. Behind me are the days of guess and check.

  • @winstoniskandar4554
    @winstoniskandar4554 5 лет назад +15

    "It only took math skills"
    Me: yeaa..............

  • @emmanuel489
    @emmanuel489 5 лет назад +1

    Almost 10 years later and ur still better than all my math teachers that I have ever had

  • @husbbi7153
    @husbbi7153 9 лет назад +6

    What a great way of explaining this factoring,,,,,, I have come up to your video over and over, well done.... not just for this problem but way more complicated one and all start from here,,,, since i got it then the rest was easy... :)

  • @drhabab
    @drhabab 6 лет назад

    I've gone through at least 7 videos about factoring trinomials with "A" being greater than 1, this is by far the best, easiest, most efficient one I've seen!

  • @Jack-xt9pi
    @Jack-xt9pi 2 года назад +5

    Thanks for the video! It's a day before my AP calc AB exam and im unironically looking this up 😂

  • @hammertime644
    @hammertime644 5 лет назад +1

    I hope you're a highly paid teacher because you explain things well, and you're very understandable. You don't say a whole much of math-gibberish that most of us don't understand.

  • @rosie-hl6qp
    @rosie-hl6qp 9 лет назад +7

    Thanks for making this...saved me on a big homework assignment

  • @lynnnguyen7290
    @lynnnguyen7290 7 лет назад

    Bless your soul for actually showing me the easier version than what my teacher/friends taught me.

  • @juliusblom3750
    @juliusblom3750 5 лет назад +6

    "I double check visually"
    Fascinating

  • @lily70rivera
    @lily70rivera 7 лет назад

    this tutorial was so helpful and so easy to follow thank you so much. I am taking math after 20+years and you are a blessing.

  • @jaemuniy
    @jaemuniy 2 года назад +4

    Thank you so much I have a test about factoring in a couple of hours and didn't know how to factor.

  • @luzguerra8055
    @luzguerra8055 8 лет назад

    THIS IS A LIFE SAVER! Thank you so much! I had gone through at least an hour worth of different vids on this subject, and so far this is the only one that made it "click" with me! Thank you thank you

  • @lowkeysavage8362
    @lowkeysavage8362 10 лет назад +25

    Wow thank you for actually being educated

  • @mikig1207
    @mikig1207 12 лет назад

    Thank you so much for making this video! This made ALOT sense to me than my teacher's lectures. NOW EVERYTHING MAKES SENSE. I can't express in words how much I'm thankful for this video. Thank you, and have a nice day.

  • @ThinkEthan
    @ThinkEthan 5 лет назад +59

    Anyone 2019?
    Holy moly: Anyone 2020?! 🤣

    • @Erica_Love_Love
      @Erica_Love_Love 5 лет назад +1

      Yep. Brushing up on my math. I forgot how to do this stuff.

    • @lilolmecj
      @lilolmecj 5 лет назад +2

      SoFreshGirl 510 every time I think I have it I am wrong! Dang it!

    • @youssefshidid2229
      @youssefshidid2229 5 лет назад +1

      2020 now!

    • @carlaavila303
      @carlaavila303 5 лет назад +1

      Here xd

    • @Falyte
      @Falyte 5 лет назад +1

      2020

  • @nilscoe3019
    @nilscoe3019 6 лет назад

    This really helped me, thank you. I struggle a little bit with math, but now I'm one with numbers.

  • @Mg2SiO4
    @Mg2SiO4 3 года назад +4

    Wonderful explanation. Very well done. Thanks.

  • @abobadilla10
    @abobadilla10 12 лет назад

    OMG thank you so much! I looked all over the web to understand this sequence & you demonstrated it the best! THANK YOU THANK YOU THANK YOU. Saved my life!

  • @thatisme5592
    @thatisme5592 2 года назад +5

    This has been so incredibly helpful! Thank you so much!

    • @RebeccaSavell
      @RebeccaSavell  2 года назад

      You're so welcome. I'm so glad it was!

  • @Khushi-km5fi
    @Khushi-km5fi 5 лет назад

    I know this video was posted 9 years ago, but you seriously helped me a lot! I have a test tomorrow and now I understand. Thank you!!

  • @legitgamingcorps494
    @legitgamingcorps494 7 лет назад +3

    Thank you for your excellent explanation. Really helped my child. Appreciate the time you took to explain it.

  • @fearofthedark88
    @fearofthedark88 10 лет назад

    this was the most straightforward way of explaining this factoring method that i've come across. thanks!

  • @jessicacastrejon2631
    @jessicacastrejon2631 10 лет назад +12

    Thank you so much our teacher taught this today and i was confused thanks for your time :)

  • @stevematson4808
    @stevematson4808 Год назад +2

    Extremely good explanation 👍😎
    I have watched many many videos on the subject of factoring and this is the BEST !

  • @samyu986
    @samyu986 Год назад +4

    Still responding to comments after 13 years, u have my respect!

  • @kaylab6335
    @kaylab6335 6 лет назад +2

    Like literally u saved my life bc my teacher taught us and she was so confusing to everyone so ur video actually helped me understand it 100% easier than my teacher thanks

  • @sparkleyes1019
    @sparkleyes1019 3 года назад +4

    2:57 - that rule helped a lot, thanks! :)))

  • @Ash-ot2bc
    @Ash-ot2bc 3 года назад +1

    It's been 11 years since you uploaded this but thank you ma'am. Normally I grasp math pretty easily but this concept just evaded me until I found your video. Best wishes

  • @leticiamal91
    @leticiamal91 3 года назад +4

    Thank you! The one video that makes it all make sense.

  • @joshbray5036
    @joshbray5036 8 лет назад

    Man, wish I found this sooner! This is pretty helpful and you explained everything perfectly in 8 mins while I couldn't understand my math teacher over several 45 minute periods. Totally using RUclips for now on if I have a question with math. Anyways, thanks again!

  • @ofethecat259
    @ofethecat259 9 лет назад +4

    i missed a few days of school and this helped so much!! thank you!! hopefully i will ace this test coming up

  • @CRYhavoc_INK
    @CRYhavoc_INK 8 лет назад +2

    HUGE thanks! I was going to drop my class because I didn't know this method, which is a very important one, and I may have had to go down a grade level in my maths to learn all of this again (which was making me not understand some material of other chapters) Crazy right? Not even kidding you saved me. Thank you sooooo much! I cannot stress it enough!

  • @arungandhi5743
    @arungandhi5743 3 года назад +3

    thank you so much. I have a quiz tomorrow and forgot how to factor trinomials. I cannot thank you enough

  • @kichigan1
    @kichigan1 12 лет назад

    I like the clarity of thinking in your teaching. Good job, thanks.

  • @gilmiller-muro7356
    @gilmiller-muro7356 3 года назад +9

    Thank you so much for this!! Very helpful. I'm sorry to be the one to tell you that 11 years in the future you will be in a global pandemic that started with bats in China. Oh and One Direction will break up but Harry Styles has a very bright future.

    • @sfyvyrrywyhtderttteyeet4227
      @sfyvyrrywyhtderttteyeet4227 3 года назад +2

      She doesn't know......she died 2 years ago.....

    • @LeeTwentyThree
      @LeeTwentyThree 3 года назад +2

      @@sfyvyrrywyhtderttteyeet4227 Not true. She commented on her latest video 7 months ago.

    • @RebeccaSavell
      @RebeccaSavell  3 года назад +7

      I'm still kickin'. Thanks for watchin'!!!!

  • @nahidkhaled7375
    @nahidkhaled7375 4 года назад +1

    Thank you you taught me better than my dad, teachers, and math textbooks tried to.

  • @danielwonink8507
    @danielwonink8507 6 лет назад +10

    what if 'b' is negative?

    • @samerakhan1725
      @samerakhan1725 6 лет назад

      Daniel Wonink negative times negative will give you a positive. So if b’s a negative it becomes a positive after you time the negative with the negative b

    • @danielwonink8507
      @danielwonink8507 6 лет назад

      StylishhGamingz. 😂😂

  • @grim22628
    @grim22628 11 лет назад

    Thank you so much , I really couldn't understand my algebra teacher but when you explained it I was blown away by how easy it was, thanks ! :D

  • @TheShadyTiger
    @TheShadyTiger 8 лет назад +7

    But what do you do when the two red parts are NOT the same?

    • @RebeccaSavell
      @RebeccaSavell  8 лет назад +8

      Sorry for just now replying to this, ShadyTiger. When the two red parts are not the same, you can't factor it.

    • @scarletaubergine5065
      @scarletaubergine5065 7 лет назад

      ^ 'ShadyTiger' oh my god that's cute 😭💀

    • @fahdkhan3536
      @fahdkhan3536 6 лет назад +1

      The King it’s then prime

  • @cheynelawson
    @cheynelawson 7 лет назад

    You are awesome in every way. I've been struggling with this for about 2 hours and every explanation I've come across made absolutely no sense. Why on earth weren't you my teacher at school :) Thank you so much!

  • @MrJulsgard
    @MrJulsgard 10 лет назад +31

    It is evident that Jesus has sent you. Thank you

  • @alkayfost3755
    @alkayfost3755 2 года назад +1

    I wish their where more math teachers like you. My math teacher explains things like I already know how to do it when I don’t.

  • @jonsomss
    @jonsomss 7 лет назад +11

    I dont want u to worry about that this minute because i will give u the rules...
    HERE ARE THE RULES

  • @The_Resident_Cryptid
    @The_Resident_Cryptid 6 лет назад

    Thank you, ma'am. You don't know how much I needed this! I hope you have a wonderful day!

  • @laurathebookworm7615
    @laurathebookworm7615 3 года назад +3

    you, good ma'am. are an absolute life saver and im so grateful for this video. thank you so much!

  • @antoniosilva8331
    @antoniosilva8331 5 лет назад +1

    I loved the clarity of your explanations. Thank you very much for your commitment with teaching mathematics. I'm glad that you exist :)