Full transcript of “Grade 8 MATH Term 1 Week 6, 7, 8: Simplifying Rational Algebraic Expressions Part 1 | MATATAG - Q1”. Click a timestamp to open the video at that moment. Need another video? Use the YouTube transcript generator.
0:02 [Musika] Hello everyone. Welcome to Matth Esip YouTube channel where you can find free Tagalog Mathematics tutorial. Our topic for today is all about rational algebraic expressions. But before that, I encourage you to click the subscribe button kung hindi pa po kayo nakakapag-subscribe so that you will be updated pag may mga bago po tayong lessons. And for our fellow teachers, we also offer our editable PowerPoint presentations to save you time in your lesson preparation. You can check the link below or message us on Facebook. Sa mga learners naman diyan, you can check our playlist para po alam natin yung pagkakasunodsunod ng ating mga lessons. Okay. So without further ado, let's now begin with our lesson. Okay. Competency
0:48 is to simplify rational algebraic expressions. This video is divided into two parts. So you can check the next video. Yun po iyung magiging part two ng ating lesson. Okay. So for now our part one is just to simplify algebraic expressions on monomials and binomials. Okay? So first let's have a review. Can you still remember the rules of exponent on dividing monomials? Ano po yung rule natin pag nagdi-divide tayo ng monomial? Okay. We are going to use the quotient rule. Remember here in dividing monomial if we have an exponent in the numerator and we have an exponent in the denominator given that the base is the same, the variables are the same, ang gagawin lang natin is to subtract the exponent. Okay? Ito po yung ating
1:34 quotient rule pag nagdi-divide po tayo. Mapapanood niyo po ito dito sa ating video lessons on multiplication and division of monomials. All right? Okay. Let's see kung naaalala niyo pa. Let's have a warm up. I'll give you time to answer these two sets of monomials. How to divide this monomials. You can pause this video para sagutin niyo in scrap paper. And then let's check kung alam niyo pa kung paano mag-divide. Okay, I hope you are now ready. Let's see. The first one. We have here 6x cu/ 3x. All we have to do is to divide the numerical coefficient and then subtract iyung ating mga exponents. Therefore, we will get 2x 2. Why? 6 / 3 is 2. And then
2:21 3 yung exponent sa taas minus yung exponent dito po sa ating denominator which is 1. 3 - 1 equ 2. How about for the second one? We have here 12 / 4 we will get 3. And then for our exponent 5 - 2 we will get 3. And then 3 - 1 here hindi na po naisulat pero magiging 2 na po siya. So ang sasagot natin is 3a cu b². I hope nasagot niyo po ito so that we can proceed with our lesson. Yeah. And also another thing to remember is yung ating factoring techniques on polynomials. So you also need to remember this. Specifically in our lesson today, you need our common monomial factoring technique. How do we factor the GCF? You can actually watch
3:08 this kung hindi niyo pa napapanood using this video. Factoring out common monomial factor. You can check this in our playlist. Okay, let's now proceed with rational algebraic expressions. How do we simplify monomials and binomials? Okay, first thing is we have to know the definition of rational algebraic expressions. Okay, bago tayo mag-simplify, dapat malinaw po sa atin ano ba ang ibig sabihin ng rational algebraic expressions. Okay, this is now the definition. Let me read. Irrational algebraic expression is a fraction. Take note of that. Or a ratio where both the numerator and the denominator are polynomials. Okay? And the denominator is not zero. So let's have an example for this. Okay. Let's have the first
3:54 one. We have 3x / x + 2. This is an example of rational algebraic expression. Okay? Both the numerator and the denominators are polynomials. Ano pa? We also have here x² - 9 / x² + x - 6. So regardless kung ilan po yung term niya, whether binomial or trinomial, as long as polynomials po lahat yan, it is a rational algebraic expression. Yan meron din tayong 2a s b / 4ab s. So all of this are considered rational algebraic expression. Okay. Now, what are examples of not a rational algebraic expression? We have the first one. We have the square root of x + 1 all over x- 3. This one is not an algebraic
4:42 expression because of the radical here. Okay? Hindi na po siya polynomial. Another one is we have here 1 / x² + 1 / x. Now, bakit hindi ito considered na algebraic expression or rational algebraic expression? Yung denominator po natin na may 1 / x, hindi na po ito considered na polynomial. There is no variables on the denominator of a polynomial. Okay. Next one we have here x + 2y. This is not an expression. This is not an algebraic rational algebraic expression because this is already a sum. Okay. Hindi na po siya iisang rational expression lamang. Okay. Next is 5x/0. Ito po ang hindinghindi pwede because the denominator is already zero.
5:29 Ang tawag na po natin dito ay undefined terms. I repeat, if the denominator is equal to zer, it is called undefined. Okay. Proceed na po tayo sa first example on how to simplify rational algebraic expression. Okay. The first one is 12x^ 4y^ 2 / 6x² y. Okay? This is monomial over a monomial. So how do we do this? All we have to do is to remember the division of monomials. I ating quotient rule. Okay? If we can divide the coefficient, just divide it directly. So if we have here 12 uh divided by 6 we will get 2. Next one. Anong gagawin natin sa mga ah ating exponents? Kapag nandito sa numerator mas mataas yung kanyang exponent all we
6:16 have to do is to subtract yung nasa baba. So 4 - 2 is 2. Next one we have 2 minus yung ating exponent dito na 1 we will get y 1. Okay? All you have to do is to divide. Okay. Kapag uh kaya naman po nating i-divide directly. Next one we have here number two, we have another monomial over a monomial. This one is 5a² b^ 4 / 15a cu b². How about this? Hindi natin kayang i-divide si 5 by 15. Ang gagawin lang natin dito is to simplify just like what we are doing in simplifying fractions. And that is to get the common factors. Okay? So pwede nating kunin yung mga factors muna sa numerator and then yung mga factors
7:02 natin sa denominator. Tsaka natin i-simplify, i-cross out or i-cancel out yung mga common factors. Okay. So ano iyung mga factors ng ating numerator? We can do our prime factorization wherein talagang ida-disect natin yung lahat ng kanilang factors. Okay? So we have here five. There is no more factor for 5. How about a squ? We have a okay how about b^ 4 we have b * b * b * b. Okay? 4 times. How about 'yung nandito sa baba? We have 15. Anong mga factors ng 15? We have 5 * 3. And then anong factors ng a cu we have 3a multip to itself. Next we have b s dalawang b. Okay? And then afterwards
7:50 we can now cancel out yung mga common factors natin. So we have here five. Meron din dito sa denominator. Cross out natin yan. And then ano pa po ang mga parehas? We have here A and then A din sa baba. Another set of A. And then 'yung B. Ah ilang B po ang nandito sa baba? We have 2 B sa taas, dalawang B din po sa baba. So yun po yung mga pwede nating i-cancel out. Or meron din po tayong ibang way mas madali, mas mabilis wherein you can just get the common factors na hindi naman kailangang prime. Okay? So halimbawa dito sa numerator we have here five and then sa baba we have here 5 and 3. But for our variables, we can just write there a squasi dito sa
8:35 baba we can actually factor out yung a s a. And remember a s a is still a cub. However, we don't need to factor out the primes isa-isa kasi all we have to do is to find yung common factor. And the common factor here is a squ. Ano pa po? Yung b we can just factor out b s b s para po merong partner si b squ sa baba. Okay. In that way hindi na natin kailangang isa-isahin. Pwede na tayong mag-cancel out dito. 5. Pwede na rin 'yung a squ pwede na rin yung b squed. Ang maiiwan na lang po dito is b s and then a. Okay? Pati na rin po yung 3. So yung mga naiwan na hindi na-cancel out
9:20 yun na po yung ating sagot. So we have again kung ito pong method ang ginamit natin dalawang B which means B s and then we have here 3 and then A. Kung ito naman ang ginamit nating method straight we can have B squ and then we have 3 and a as well. So our answer is b s over 3a. Okay. Again, I repeat our answer is b² / 3a. [Musika] ت [Palakpakan]
10:08 [Musika] Okay, for example number 3, we have here 4x² / 6x² - 8x. So we now have here a monomial in the numerator and then we have here a binomial in the denominator. So I suggest ano kaya ang una nating isi-simplify or ifctor dito? I suggest yung mas mahaba. In this case, ang nasa denominator is binomial. So kung ano po yung mas mahabang polynomial, 'yun ang lagi nating unahin ano. So we have here 6x² - 8x. Anong klaseng technique or factoring technique kaya ang magagamit natin dito? Meron ba kayong nakikitang
10:55 common sa dalawa? Ah yung tinatawag nating common monomial factor. So dito lagi nating unahin yung technique na factoring out the common monomial factor. Ano kaya ang pwede nating i-divide sa first term na pwede ring i-divide sa second term? Yun na po yung tinatawag nating GCF. And how do we do that? If we're going to apply the prime factorization method, we can start by factoring out yung 6 or yung numerical coefficient. Anong factor ni 6? We have 2 and 3. Ano rin po ang factor ni x s? We have 2x. X. Ano po ang factor ni 8? We have 2 and 4. And then anong factor ng x? Wala po since mag-isa lang siya. Next, ano yung common dito sa mga
11:41 factors nila? You can uh you can copy yung mga common which is 2 and then x. So yung 2x yun na po yung ating gcf. Okay? Yung tinatawag nating greatest common factor. Now how about sa taas? Pwede ba nating i-factor out yung 4x s? Pwede pa. So we can actually have 2 for 4 since 2 * 2 is 4. And then we have here x s no magagamit natin to. As long as kaya pa nating i-factor out yung maliit na term or yung monomial, pwede pa nating i-factor out pero i-prioritize po natin yung mas mahaba. Okay? Another method is you just need to get the common greatest
12:28 common factor which is yung GCF which is yung 2x no. 2x and then anong maiiwan dito sa binomial natin? We can have 3x - 4. Okay? Saan po galing yung 3x - 4? Galing po siya dito sa mga hindi natin kinuha as GCF. So we have 3x and then we have - 4. That's why we have here 3x - 4. Na-factor out natin yung GCF which is 2x. Nilabas po natin sa parenthesis. Ang naiwan sa parenthesis is 3x - 4. Para masigurado natin kung tama ito, we can distribute ito. 2x * 3x, is it 6x²? Yes. 2x -4 is it -8x? Yes. Tama po itong ating factors. Now, sa numerator, we can
13:15 just have 2x * 2x. Okay? Because 2x * 2x is 4x². Okay. Now, since parehas po 'yung 2x tsaka sa numerator tsaka sa denominator, cancel out po natin 'yan. At ang maiiwan na lang is 'yung 2x sa taas and then 3x - 4 sa baba. So, our final answer is 2x / 3x - 4. So again, kailangan ba nating i-apply lahat itong mga prime factorization natin? Hindi po kailangan. There will be a point na sa practice uh through your practice magiging automatic na po yan. You can go straight from this point na pagtingin niyo pa lang is makikita niyo kaagad yung mga factors niya and then there
14:01 will be a point na alam niyo na rin kaagad kung ano yung final answer. You just need to practice. Okay. Let's have example number four. We have here 5y + 25 all over 10y + 50. In this case, we have here a binomial all over a another binomial. So, how do we simplify this? Ah, meron ba tayong kailangang i-factor out na common monomial factor? Yun po lagi ang uunahin natin. I-prioritize natin ang factoring technique na common monomial factor. Yes, sa numerator meron pong common na factor diyan which is actually 5. Okay, because 5 if you multiply 5 by y + 5 * y is 5y and 5 * 5 is 25. Okay. So again,
14:49 you factor out the common monomial factor or the GCF which is 5. And then kung ano po 'yung maiiwan 'yun po 'yung nasa loob ng parenthesis. You can also do that. Pag nakuha niyo na 'yung GCF, you can also divide kung ano 'yung nasa first term natin. Halimbawa, 5y / 5, that's the uh answer here, which is y. And then 25 / by the GCF which is 5. You will also get here the second term. Okay? Ganun lang po siya. Next we have here 10y + 50. Ano po ang common sa dalawa? Ah, can we have 10? Okay, pwede po ang 10 because if you factor out 10y ah you will get 10 * y. And then if you factor out uh 50 ah ano po yung mga factors niya? You can also have 10 * 5
15:34 it will be 50. Next, meron na pong parehas sa numerator and sa denominator. We can just cross this out which is yung y + 5 natin. Meron ding y + 5 dito. So ang maiiwan na lang po ay yung 5 all over 10. Is this our final answer? Hindi po. Pwede pa natin siyang i-simplify. So 5 / 10 is actually 1/2. All right. By dividing both the numerator and the denominator by 5, you will get 1/2. Okay, let's have the last example. Example number 5, we have here 3a S- 6a all over 2a- 4. Okay, let's start with the numerator. Ano po ang ating GCF dito sa dalawang term? So, since may common tayong mga factors diyan, our GCF is 3a.
16:23 Okay? And maiiwan sa parenthesis natin is a - 2. Okay, let's check. 3a * a is 3A². Tama. And then 3a * -2 is -6a. Tama po iyung ating mga factors. Now, sa baba naman po, ano po ang common kay 2a tsaka 4? The common or the GCF is 2. Okay? Because if we multiply it by a, we will get 2a. If we multiply 2 by -4, we will also get uh I mean if we multiply 2 by -2, we will get -4. Okay. Ang common po sa numerator and denominator, we can cross it out. A - 2. And then ang maiiwan is 3a sa taas and then 2 sa baba. Okay. Can we still uh simplify
17:09 this 3 / 2? No. Hindi po. So our final answer is just 3a / 2. Okay. Let's now proceed to the exercises. We have here five algebraic expressions for you to practice with. Bigyan ko po kayo ng time para masagot to. You can pause this video and then do this on your own and then you can come back later para po makita niyo yung ating solution. Okay? I hope makuha niyo po yung tamang sagot. God bless sa pagsagot. Okay, if you are now ready, I'm now going to show the simplified form of this rational expressions. Okay, we have
17:54 the first one. It is 2x s y. And for number two, we have ab / 2. And then number 3, we have x s / 2x - 3. And then for number 4 we have here 2. And then lastly for number 5 just 2a. Okay. So this are just the final answer. Pero yung solutions po natin dito, we we are now going to apply yung mga uh factoring technique po na napag-aralan natin previously. So I hope nakuha niyo po ng tama yung mga sagot dito. And then for our next lesson, we will be having the simplifying rational algebraic expressions pa rin part two. This will now be about binomials and trinomials,
18:40 including iyung mga factoring technique natin for special products. Okay? But before I go, I will be leaving here another set of activity for you to practice with. Okay, I will not be sharing the answers for this one, but you can share your inputs in the comment section or if your teacher is using this PowerPoint, you can just check your activity later on. As of now, thank you for listening and I hope to see you again on the next video. God bless and byebye for now. Kung meron kang natutunan sa video na ito, please click the subscribe button to support this channel para mas matulungan ulit kita sa mga susunod mo pang matth lessons. Lagi mong tatandaan ang matth ay para sa lahat at ako si teacher Van.
19:26 Nagsasabing dito sa mat isip lamang ang nag-iisip. God bless and see you on the next video. [Musika]
