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Chrissy
9/7/2023
Algebra 1
Polynomials and Multiplying Polynomials
108
•
Sep 7, 2023
•
Easy Steps to Add, Subtract, and Multiply Polynomials for Kids
Chrissy
@vophanim
1 / 2
Multiplying Polynomials
This page covers various methods for multiplying polynomials, including multiplying a monomial by a polynomial, binomial by binomial (FOIL method), and any polynomial by any polynomial.
Monomial and Polynomial Multiplication
To multiply a monomial by a polynomial:
- Use the distributive property to multiply the monomial by each term of the polynomial.
- Write your answer in standard form.
Example: 4x² (3x² - 8x - 5) = 12x⁴ - 32x³ - 20x²
Binomial by Binomial Multiplication (FOIL Method)
To multiply two binomials:
- Use the FOIL method (First, Outer, Inner, Last).
- Combine like terms and write your answer in standard form.
Example: (x + 3)(2x - 1) = 2x² + 5x - 3
Definition: FOIL - An acronym representing the steps for multiplying two binomials: First, Outer, Inner, Last.
Any Polynomial by Any Polynomial
To multiply any two polynomials:
- Multiply each term from the first polynomial by each term in the second polynomial.
- Combine like terms and write your answer in standard form.
Example: (x + 2)(x² - 3x - 8) = x³ - x² - 14x - 16
These Multiplying polynomials step-by-step instructions provide a comprehensive guide for various polynomial multiplication scenarios. They can be used alongside Multiplying Polynomials Worksheets with answers PDF or as a reference when working on Multiplication of Polynomials Worksheet with answers.
Highlight: The color-coded examples in this guide serve as effective Color coded examples of polynomial operations, helping students visualize the steps more clearly.
By mastering these techniques, students will be well-equipped to handle Multiplying polynomials examples with answers and tackle more complex algebraic problems involving polynomial multiplication.
Adding and Subtracting Polynomials
This page provides instructions for adding and subtracting polynomials, which are essential skills in algebra. The process involves combining like terms and presenting the result in standard form.
Adding Polynomials
To add polynomials, follow these steps:
- Combine like terms together.
- Write your answer in standard form (decreasing order of degree).
Example: (4x² + 1 - 9) + (7x⁴ - 9x² + 48)
Solution: 7x⁴ - 5x² + 40
Highlight: When adding polynomials, it's crucial to identify and combine like terms correctly.
Subtracting Polynomials
To subtract polynomials, follow these steps:
- Turn the subtraction into an addition problem by changing the subtraction sign to addition between the two polynomials.
- Reverse the sign of each term in the second polynomial.
- Add like terms together.
- Write your answer in standard form.
Example: (3x² - 6x - 9) - (2x² + 8x - 3)
Solution: x² - 14x - 6
Vocabulary: Standard Form - A way of writing polynomials with terms arranged in descending order of degree.
These Adding and Subtracting Polynomials instructions provide a clear, step-by-step approach to mastering these fundamental algebraic operations. By following these guidelines, students can effectively solve problems on an Adding and Subtracting Polynomials worksheet or use them as a reference when working with an Adding and Subtracting polynomials Calculator.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Easy Steps to Add, Subtract, and Multiply Polynomials for Kids
Chrissy
@vophanim
Adding and subtracting polynomials, as well as multiplying them, are fundamental algebraic operations. This guide provides step-by-step instructions for these processes, including examples and color-coded explanations to enhance understanding. The methods cover adding and subtracting polynomials, multiplying monomials with polynomials,... Show more
Multiplying Polynomials
This page covers various methods for multiplying polynomials, including multiplying a monomial by a polynomial, binomial by binomial (FOIL method), and any polynomial by any polynomial.
Monomial and Polynomial Multiplication
To multiply a monomial by a polynomial:
- Use the distributive property to multiply the monomial by each term of the polynomial.
- Write your answer in standard form.
Example: 4x² (3x² - 8x - 5) = 12x⁴ - 32x³ - 20x²
Binomial by Binomial Multiplication (FOIL Method)
To multiply two binomials:
- Use the FOIL method (First, Outer, Inner, Last).
- Combine like terms and write your answer in standard form.
Example: (x + 3)(2x - 1) = 2x² + 5x - 3
Definition: FOIL - An acronym representing the steps for multiplying two binomials: First, Outer, Inner, Last.
Any Polynomial by Any Polynomial
To multiply any two polynomials:
- Multiply each term from the first polynomial by each term in the second polynomial.
- Combine like terms and write your answer in standard form.
Example: (x + 2)(x² - 3x - 8) = x³ - x² - 14x - 16
These Multiplying polynomials step-by-step instructions provide a comprehensive guide for various polynomial multiplication scenarios. They can be used alongside Multiplying Polynomials Worksheets with answers PDF or as a reference when working on Multiplication of Polynomials Worksheet with answers.
Highlight: The color-coded examples in this guide serve as effective Color coded examples of polynomial operations, helping students visualize the steps more clearly.
By mastering these techniques, students will be well-equipped to handle Multiplying polynomials examples with answers and tackle more complex algebraic problems involving polynomial multiplication.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Adding and Subtracting Polynomials
This page provides instructions for adding and subtracting polynomials, which are essential skills in algebra. The process involves combining like terms and presenting the result in standard form.
Adding Polynomials
To add polynomials, follow these steps:
- Combine like terms together.
- Write your answer in standard form (decreasing order of degree).
Example: (4x² + 1 - 9) + (7x⁴ - 9x² + 48)
Solution: 7x⁴ - 5x² + 40
Highlight: When adding polynomials, it's crucial to identify and combine like terms correctly.
Subtracting Polynomials
To subtract polynomials, follow these steps:
- Turn the subtraction into an addition problem by changing the subtraction sign to addition between the two polynomials.
- Reverse the sign of each term in the second polynomial.
- Add like terms together.
- Write your answer in standard form.
Example: (3x² - 6x - 9) - (2x² + 8x - 3)
Solution: x² - 14x - 6
Vocabulary: Standard Form - A way of writing polynomials with terms arranged in descending order of degree.
These Adding and Subtracting Polynomials instructions provide a clear, step-by-step approach to mastering these fundamental algebraic operations. By following these guidelines, students can effectively solve problems on an Adding and Subtracting Polynomials worksheet or use them as a reference when working with an Adding and Subtracting polynomials Calculator.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user