Penjumlahan, Pengurangan, dan Perkalian Suku Banyak Polinomial | Matematika SMA

Summary

This educational video offers a comprehensive guide to polynomial operations, including addition, subtraction, and multiplication, which are fundamental algebra concepts revisited from middle school to high school. The host demonstrates how to combine like terms and perform distributive multiplication with step-by-step examples, such as adding 3x^2 + 5x and x^3 - 2x + 9, subtracting polynomials, and multiplying polynomials. The video is designed to clarify the differences between polynomial operations and aims to make algebra more accessible. Viewers are encouraged to like, comment, and subscribe for more mathematical lessons.

Takeaways

• 📘 This video tutorial focuses on teaching the operations of adding, subtracting, and multiplying polynomials, which are also known as 'suku banyak' in high school algebra.
• 🔢 The first operation demonstrated is the addition of polynomials, specifically (3x² + 5x) + (x³ - 2x + 9), emphasizing the combination of like terms.
• ➕ The result of the addition is simplified to x³ + 3x² + 3x + 9, showcasing the process of combining like terms and simplifying the expression.
• ➖ The subtraction operation is also covered, with an example of subtracting (3x² + 5x) from (x³ - 2x + 9), detailing the distribution of the negative sign across terms.
• 🔄 The difference between P - Q and Q - P in polynomial subtraction is highlighted, showing how changing the order affects the signs of the terms.
• 📐 The multiplication of polynomials is explained through the distributive property, using the example of (3x² + 5x) multiplied by (x³ - 2x + 9).
• 📘 The tutorial emphasizes the importance of arranging terms in descending order of their degree after performing operations, which is a key step in polynomial arithmetic.
• 📝 The process of multiplying polynomials involves multiplying each term of one polynomial by each term of the other, then combining like terms to simplify the result.
• 📊 The video provides a step-by-step guide on how to handle each power of x when performing polynomial operations, ensuring clarity for learners.
• 👍 The video encourages viewers to like, comment with questions, and subscribe for more educational content on mathematics.

Q & A

What is the main topic of the video?

The main topic of the video is learning how to add, subtract, and multiply polynomials, which are also known as algebraic expressions.

What are the terms used for polynomials in high school compared to middle school?

In middle school, polynomials are referred to as 'Aljabar,' while in high school, they are called 'suku banyak' or 'polynomials' with an emphasis on higher degrees.

What is the first operation demonstrated in the video?

The first operation demonstrated in the video is the addition of polynomials, specifically 3x^2 + 5x and x^3 - 2x + 9.

How is the addition of polynomials performed according to the video?

The addition of polynomials is performed by combining like terms, starting from the highest degree to the lowest, and simplifying the expression.

What is the result of adding the polynomials 3x^2 + 5x and x^3 - 2x + 9?

The result of adding the polynomials 3x^2 + 5x and x^3 - 2x + 9 is x^3 + 3x^2 + 3x + 9.

What is the second operation covered in the video?

The second operation covered in the video is the subtraction of polynomials.

How does the video demonstrate the subtraction of polynomials?

The video demonstrates the subtraction of polynomials by distributing the negative sign across the terms of the polynomial being subtracted and then combining like terms.

What is the difference between the operations of polynomial subtraction when PX - QX and QX - TX?

The difference lies in the order of the polynomials being subtracted and the sign of each term in the polynomial that is being subtracted.

What is the final operation taught in the video?

The final operation taught in the video is the multiplication of polynomials, specifically the distributive property in the context of polynomial multiplication.

How is the multiplication of polynomials explained in the video?

The multiplication of polynomials is explained by using the distributive property, multiplying each term of one polynomial by each term of the other and then combining like terms.

What is the final expression obtained after multiplying the polynomials 3x^2 + 5x and x^3 - 2x + 9?

The final expression obtained after multiplying the polynomials 3x^2 + 5x and x^3 - 2x + 9 is 3x^5 - 6x^4 + 17x^3 - 10x^2 + 45x.

What is the call to action for viewers at the end of the video?

The call to action for viewers is to like the video if they enjoyed it, leave comments if they have questions, and subscribe for more math lessons.

Outlines

00:00

📘 Polynomial Operations Overview

This paragraph introduces the concept of polynomial operations, including addition, subtraction, and multiplication. It explains that these operations are a continuation of algebra learned in middle school but are reviewed in high school with a focus on 'suku banyak' or 'many terms.' The paragraph sets the stage for a detailed explanation of how to perform these operations with polynomials, starting with the addition and subtraction of polynomials represented by 'PX' and 'QX'.

05:01

🔢 Detailed Polynomial Addition and Subtraction

The paragraph demonstrates the process of adding and subtracting polynomials through a step-by-step example. It begins with the addition of 'PX' (3x² + 5x) and 'QX' (x³ - 2x + 9), showing how to combine like terms and simplify the expression to x³ + 3x² + 3x + 9. It then moves on to subtraction, illustrating how to handle the negative signs and combine like terms to obtain -x³ + 3x² + 7x - 9. The paragraph also covers the subtraction of 'QX' from 'TX' and vice versa, highlighting the differences in the outcomes and emphasizing the importance of correctly handling the signs and terms during the operations.

📐 Multiplication of Polynomials

This paragraph delves into the multiplication of polynomials, focusing on the distributive property to multiply 'PX' (3x² + 5x) by 'QX' (x³ - 2x + 9). It breaks down the process into individual term multiplications, such as 3x² * x³ resulting in 3x⁵, and then combines the products, taking into account the signs and like terms. The final result of the multiplication is a detailed polynomial expression, showcasing the comprehensive approach to polynomial multiplication.

👍 Engaging with the Content

The final paragraph encourages viewers to like the video if they found it helpful, leave comments with any questions, and subscribe for more educational content on mathematics. It ends with a warm and inclusive note, wishing viewers well and expressing a desire to meet them in the next video, reinforcing the community aspect of learning and engaging with the content.

Keywords

💡Polynomial

A polynomial is an algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, and non-negative integer exponents of variables. In the video, polynomials are the main objects of study, with operations like addition, subtraction, and multiplication being demonstrated using polynomials such as '3x² + 5x' and 'x³ - 2x + 9'.

💡Algebra

Algebra is a branch of mathematics that uses symbols and rules to manipulate and solve equations. The video script mentions that the concepts being taught were previously learned in middle school under the subject of algebra but are revisited in high school with a focus on 'suku banyak' or polynomials.

💡Like Terms

Like terms are terms in a polynomial that have the same variable raised to the same power. In the video, when adding or subtracting polynomials, like terms are combined. For example, '3x²' and '5x' are like terms because they both contain the variable 'x' raised to the same power.

💡Exponent

An exponent indicates the number of times a base is multiplied by itself. In the context of the video, exponents are used to express the power to which a variable is raised, such as 'x³' indicating 'x' multiplied by itself three times.

💡Distributive Property

The distributive property is a fundamental algebraic property that allows for the multiplication of a term by a polynomial by multiplying the term by each term of the polynomial separately. In the video, this property is used when multiplying '3x² + 5x' by 'x³ - 2x + 9', where each term of the first polynomial is multiplied by each term of the second.

💡Addition

Addition in algebraic expressions involves combining like terms by adding their coefficients. In the script, the addition of polynomials '3x² + 5x' and 'x³ - 2x + 9' is demonstrated, resulting in 'x³ + 3x² + 3x + 9'.

💡Subtraction

Subtraction in polynomials is similar to addition but involves taking the opposite of the coefficients of the terms being subtracted. The video shows the subtraction of 'x³ - 2x + 9' from '3x² + 5x', resulting in 'x³ - 3x² + 7x - 9'.

💡Multiplication

Multiplication of polynomials involves using the distributive property to multiply each term of one polynomial by each term of the other. The video demonstrates this by multiplying '3x² + 5x' with 'x³ - 2x + 9', resulting in a new polynomial.

💡Simplify

Simplifying a polynomial involves combining like terms and reducing the expression to its most concise form. The video script mentions simplifying after combining like terms, such as reducing '3x² + 5x - 2x' to '3x² + 3x'.

💡Constant Term

A constant term in a polynomial is a term that does not contain any variables. In the video, '9' is a constant term in the polynomial 'x³ - 2x + 9'. Constants are often the last terms to be combined when simplifying polynomials.

Highlights

Introduction to polynomial operations: addition, subtraction, and multiplication.

Review of polynomial operations, previously learned in middle school and revisited in high school.

Explanation of like terms and their importance in polynomial addition.

Demonstration of adding polynomials: combining like terms and simplifying.

Example given: adding polynomials 3x² + 5x and x³ - 2x + 9.

Step-by-step process of polynomial addition, focusing on like terms.

Result of the addition: x³ + 3x² + 3x + 9.

Introduction to polynomial subtraction, with an emphasis on distributing the negative sign.

Example given: subtracting polynomials 3x² + 5x from x³ - 2x + 9.

Step-by-step process of polynomial subtraction, including distributing the negative sign.

Result of the subtraction: x³ - 3x² + 7x - 9.

Difference between polynomial subtraction when subtracting in different orders.

Introduction to polynomial multiplication, using the distributive property.

Example given: multiplying polynomials 3x² + 5x with x³ - 2x + 9.

Step-by-step process of polynomial multiplication, applying the distributive property.

Result of the multiplication: 3x⁵ - 6x⁴ + 17x³ - 10x² + 45x.

Encouragement to like the video and subscribe for more math lessons.

Transcripts

Hai Halo Assalamualaikum apa kabarnya di

video kali ini kita akan belajar cara

menjumlahkan mengurangkan dan juga

mengalihkan polinomial atau suku banyak

ini sebenarnya udah kalian pelajari di

SMP ya nama lainnya itu Aljabar tapi di

SMA diulangin lagi dengan nama suku

banyak jadi pangkatnya untuk udah lebih

besar ya Oke Langsung aja ya kita jawab

yang pertama yang a adalah dia minta

yang pertama adalah PX ditambah dengan

qx

ya kita lihat di sini px-nya adalah

3x² + 5x

sedangkan qx-nya adalah

x ^ 3 - 2x + 9 ini kita jumlahkan saja

berdasarkan suku yang sejenis ya Jadi

kita kumpulkan mulai dari pangkat yang

paling besar di sini pangkat paling

besar adalah x ^ 3

lalu x ^ 2 ya 3X ^ 2

ada lagi pangkat 2 nggak ada ya kita

lanjut ke yang X saja

di sini 2x depannya negatif kita tulis

juga negatif ya

lalu yang angka saja atau konstanta lalu

ketika bisa kita Sederhanakan kita harus

Sederhanakan x ^ 3 di sini sendirian ya

kita nggak perlu hitung ya karena dia

sendirian

Begitu juga dengan x pangkat 2 juga

sendirian nah yang ini sama-sama x ini

bisa kita hitung ya 5 dikurang 2 berarti

3

lalu 9nya konstantanya sendirian maka

jawabannya adalah ini ya jadi x ^ 3 + 3X

^ 2 + 3X + 9 Oke kita lanjut yang

pengurangan ya TX dikurang qx

kita Tuliskan lagi TX nya adalah 3x²

+ 5x - dengan

oke nah untuk pengurangannya kita buka

dulu tanda kurangnya ya tanda kurungnya

di sini kita buka sehingga yang di sini

jadi 3x² + 5x - ketemu x ^ 3 jadi

negatif x pangkat 3 negatif ketemu

negatif jadi positif 2x - ketemu positif

jadi negatif 9 lalu sama seperti tadi

kita pindahkan dulu pangkat yang paling

besar ya di sini negatif x pangkat 3

negatifnya jangan lupa ya lalu di sini

yang pangkat 2

positif

lalu di sini 5 + 2 jadi 7 ya 7x lalu

yang terakhir -9 ini untuk yang PX - QX

kita lanjut ya kita lanjut ke yang QX -

TX ini kita balik ya jadi qs-nya dulu

kita kurang dengan PX qx-nya adalah x ^

3 - 2x + 9 dikurang tx-nya 3x² + 5x sama

seperti tadi kita buka dulu tanda

kurungnya ya X ^ 3 - 2X + 9 - 3x²

orang ketemu plus kurang 5 x lalu kita

Sederhanakan ya jadi x ^ 3 nya sendirian

lalu di sini yang pangkat duanya

-3x ^ 2 lalu yang x-nya -2 ini -5 jadi

-7x + 9 jadi ada perbedaan antara P

dikurang Q dan Q dikurang X ya

perbedaannya terlihat jelas ya oke yang

terakhir yang D lanjut ini adalah PX

dikali dengan QX

PX dikali dengan

QX ya

px-nya adalah 3x²

+ 5x yang kita kali dengan qx-nya adalah

x ^ 3 - 2x + 9 ini kali sebar ya

distributif kita kali sebar saja yang

3x² dulu ya 3x² kita kali dengan yang di

sini temannya ya X ^ 3 - 2X + 9 lalu

operasinya adalah tambah 5 X dikali juga

Sama ya X ^ 3 - 2X + 9 lalu kita bisa

hitung ya

kita hitung hasilnya

3x² * x ^ 3 jadi 3x nya pangkatnya kita

tambahkan ya jadi x ^ 5 ini 3x² dikali

negatif berarti negatif 3 dikali 2 6 x

nya jadi pangkat 3 ya ini pangkat 2 ini

pangkat 1 jadi pangkat 3 ditambah nih 3

* 9 27 x ^ 2 lalu yang sebelahnya ya 5

x ^ 4 nih pangkatnya ya lalu 5 jadi - ya

25 dikali 2 10 x pangkat 2 lalu satu

lagi ke bawah aja ya 5x * 9 itu tambah

45 ya X nah lalu kita kumpulkan

berdasarkan suku yang sejenis pangkat

paling besar adalah pangkat 5 ya kita

tulis 3x ^ 5 enggak ada lagi ya pangkat

5 lalu pangkat 4 pangkat 4 nya sendirian

juga ditambah 5 x ^ 4 lalu yang pangkat

3 juga sendirian dikurang 6 x ^ 3 ^

2-nya ada dua ya ini 27 sama -10 ya 27 -

10 itu

17x² lalu yang X saja ditambah

45x ya

jadi seperti itu ya cara untuk

menambahkan

mengurangkan dan juga mengalikan dari

persamaan suku banyak atau polinomial

silahkan like jika suka video ini jika

ada pertanyaan boleh tinggalkan di kolom

komentar dan jangan lupa juga untuk

subscribe agar tahu cara menghitung

pelajaran matematika yang lain sampai

ketemu di video selanjutnya

wassalamualaikum warahmatullahi

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