Wednesday, September 28, 2016

Middle School Math Solutions – Polynomials Calculator, Multiplying Polynomials

Multiplying polynomials can be tricky because you have to pay attention to every term, not to mention it can be very messy. There are a few ways of multiplying polynomials, depending on how many terms are in each polynomial. In this post, we will focus on how to multiply two term polynomials and how to multiply two or more term polynomials.

Multiply two term polynomials

When multiplying polynomials with two terms, you use the FOIL method. The FOIL method only works for multiplying two term polynomials. FOIL stands for first, outer, inner, last. This lets you know the order of how to distribute and multiply the terms. Let’s see how it works.


After FOILing, multiply the terms, group like terms, and add like terms if there are any.
Here is another helpful identity to use when multiplying two term polynomials:
(a+b)(a-b)=a^2-b^2
Multiplying these polynomials is pretty simple because if you memorize these identities then you just plug in the values and have an answer.

Multiplying multiple term polynomials

You cannot use the FOIL method to multiply these polynomials. Instead, you have to multiply each term in one polynomial by each term in the other. You can do this by multiplying each term of one polynomial by the other polynomial. This can be tricky because it is easy to miss one term. When we do examples of this, it will become easier to understand how to solve them.

When multiplying polynomials, you may come across multiplying variables with exponents by variables with exponents. In this case, we use this exponent rule:
x^n\cdot x^m=x^(n+m)
For this rule, the base or variable must be the same. When multiplying variables with exponents, you add the exponents together.


Let’s see some examples to understand how to multiply polynomials.
First example (click here):
(2x-1)(5x-6)
We will use the FOIL method to solve this.
1.   Use FOIL identity
(2x-1)(5x-6)
2x\cdot 5x+2x\cdot -6+(-1)\cdot 5x+(-1)\cdot -6
2.   Multiply terms
10x^2-12x-5x+6
3.   Group like terms
10x^2-12x-5x+6
 (Luckily, everything was already grouped together)

4.   Add like terms
10x^2-17x+6

Next example (click here):
(2x^2+6)(2x^2-6)
Here, we can use another one of the identities for multiplying two term polynomials.
1.   Use (a+b)(a-b)=a^2-b^2
(2x^2+6)(2x^2-6)
(2x^2 )^2-6^2
2.   Simplify
4x^4-6^2
4x^4-36
Last example (click here):
(x^2+2x-1)(2x^2-3x+6)
1.   Multiply each term in one polynomial by the other polynomial
x^2 (2x^2-3x+6)+2x(2x^2-3x+6)-1(2x^2-3x+6)
2.   Distribute and multiply
2x^2\cdot x^2-3x\cdot x^2+6\cdot x^2+2x^2\cdot 2x-3x\cdot 2x+6\cdot 2x+2x^2\cdot -1-3x\cdot -1+6\cdot -1
2x^4-3x^3+6x^2+4x^3-6x^2+12x-2x^2+3x-6
3.   Group like terms
2x^4-3x^3+6x^2+4x^3-6x^2+12x-2x^2+3x-6
2x^4-3x^3+4x^3+6x^2-6x^2-2x^2+12x+3x-6
4.   Add like terms
2x^4+x^3+6x^2-6x^2-2x^2+12x+3x-6
2x^4+x^3-2x^2+12x+3x-6
2x^4+x^3-2x^2+15x-6

Multiplying polynomials looks intimidating, but as long as you keep your work neat and double check your work, it should be pretty easy. Practice will be one of the biggest things that will help you. The more you practice, the easier multiplying polynomials will be because you will get the hang and flow of how to multiply them. Check out Symbolab’s Practice for more help and practice.

Until next time,

Leah

90 comments:

  1. Thanks for sharing.I found a lot of interesting information here. A really good post, very thankful and hopeful that you will write many more posts like this one.
    https://notepad.software/
    vidmate
    https://filezilla.software/

    ReplyDelete
  2. You should know how to write a good business analyst resume! Take a close look to this guide!

    ReplyDelete
  3. For this rule, the base or variable must be the same. When multiplying variables with exponents, you add the exponents together. C1000-010 exam dumps

    ReplyDelete
  4. I was searching for something like this for quite a long time and at last I’ve found it on your blog. It was definitely interesting for all users i must want to write my paper for me appreciate your thoughts you have already shared though this post.

    ReplyDelete
  5. I like this website pretty much. Great info. Hi and thanks for the web blogs. Expert comptable Guadeloupe

    ReplyDelete
  6. Nice Post! The weakness of Verizon Verizon Swot Analysis is that it charges more money than its competitors for providing their service.

    ReplyDelete
  7. I am reading first time about mobile massage and from the first look I consider it as the professional would be providing tips for massage to people living in remote areas. Ben Barnes Shearling Jacket Well, you come up with exciting thing for the people looking for relaxed life.

    ReplyDelete
  8. Assignment help Online provides you best support on the assignment related to management and business and business operations. Online Assignment Help

    ReplyDelete
  9. Mathematics is very tuff subject if you can not unerstand when students need help in education there are many online websites which provides math assitance forhe weak students.

    ReplyDelete
  10. We do provide many facilities to the students who are said to be pursuing their academic courses in Melbourne. Along with our qualified Melbourne tutors, the online assignment writing service also includes pre-solved question papers, sample assignments and practice manuals for the required topic. We even let the students to choose up with the assignment help, which they are in need of under different courses and subjects.
    For further information & queries, Visit our website assignment help melbourne

    ReplyDelete
  11. thank you.
    คาสิโนออนไลน์ที่น่าเชื่อถือและมีความเป็นมืออาชีพที่สุดในตอนนี้
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    ร่วมมาเป็นส่วนหนึ่งกับเว็บไซต์คาสิโนออนไลน์ของเราได้เลยค่ะ
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

    ReplyDelete
  12. We are prepared to deliver reliable and trusted Write My Research Papers services in all the outlined levels of study due to the many experts that we have in our company. Our College Research Paper is affordable and cheap as well for students who have very limited cash flows, and their budgets are usually constrained.

    ReplyDelete
  13. When students don’t have enough time to complete their assignments they search for online writes to write my assignment for me. In that case, they can get instant help from expert writers of Myassignmenthelp.com to when they request to write my assignment. The life of a student involves the dilemma of preparing multiple assignments at once like homework, dissertation, thesis paper, research paper and more. Well, you can be sure that your prayers have been heard, as MyAssignmenthelp.com is here to salvage your academic performance.

    ReplyDelete
  14. The dissertation can be influenced by many things, which one of them is the length of the work. Writing dissertation is the way to show your expertise on a certain subject, but it should maintain some courtesies in order to present them in front of a dissertation committee. The length factor could be a great impact while evaluating dissertations. So one should be careful about the length and have a fair idea of what be an average length of a dissertation. To get a great idea regarding the perfect length of a dissertation paper, click here and get assistance.

    ReplyDelete
  15. Your blog is very good and very informative. Your blog post is very useful. It is exceptionally accommodating for me I learn new information from your post. I truly love your blog post.Thank you for sharing this post with us keep it up.Students always asking us how to write an annotated bibliography in USA? What we suggest them is to hire assignment helper from 500+ writers online which were write your assignment with the help of best free plagiarism checker . For More Detail : Harvard Referencing generator

    ReplyDelete
  16. StudentsAssignmentHelp.com provides the best services of Do My Assignment Help. Get your Assignment Services at the best price and improve your grades. Our 3000+ Expert writers provide the best services of Assignment Writing for all College students. For more information contact here- +44-755-536-9184.or [email protected]

    ReplyDelete
  17. Translation Services Singapore is striving towards creating a great academic translation platform to the college and universities students so they can easily understand the subject matter. Our high experienced team of professional translators avails 24X7 for authentic translation help in desired languages.

    ReplyDelete
  18. Are you under the stress due to tight deadline and essay submission? Your search for finding the expert who can "write my essay online" ends here at EssayAssignmentHelp.com.au.
    Students come to us and say “I can pay for essay writer, but I need high-quality essay”. If you are one of those, we are here to help you out.
    Don’t lose your academic grades, just hire the best essay editors and proofreaders for your essay for both school and college level.

    ReplyDelete
  19. In a time when students are daily pressed for custom assignment writing service and multiple meeting multiple deadlines and keeping up with classes, the tempo to reflect on one’s own achievements and developments as a student and person, might be difficult to come by. Especially during those crucial times when students require and search for admissions essay help and ‘tips on college essays’ on the internet, it becomes strategically imperative to reevaluate one’s own personal development in an ordered way. If you need assignment help, just ask us to do my essay. Very often students fail to deliver essays that keep a fair level of balance between their personal and extra-curricular achievements and their academic development. Know more about information technology assignment help.

    ReplyDelete
  20. With our 360 IT Assignment Help services, you can quickly sort out all such problems. For your aid, we have even simplified our order processing steps. So now all our excellent assistive services are yours to avail without any complication.

    ReplyDelete
  21. A good blog always comes-up with new and exciting information and while reading I have feel that this blog is really have all those quality that qualify a blog to be a one write my essay

    ReplyDelete
  22. Are you looking to hire the best Custom Research Paper Services? It is tedious and overwhelming crafting Research Paper Assistance Services for learners, Custom Dissertation Writing Service can be basic complex with detailed instructions from the teacher.

    ReplyDelete
  23. Professional Online Thesis Writing Services, avail the best help for your Thesis Writing here at AssignmentStudio.

    ReplyDelete
  24. Are you looking to hire the best Custom Research Paper Services? It is tedious and overwhelming crafting Research Paper Assistance Services for learners, Custom Dissertation Writing Service can be basic complex with detailed instructions from the teacher.

    ReplyDelete
  25. At MyAssignmenthelp.com, we understand that attending a nursing course can be more taxing than it seems. You don’t just need to study and appear for tests. You also need to prepare a number of assignments and tasks, including nursing dissertations. And if you cannot spare enough time for these tasks, it won't be possible for you to pnurepare a remarkable paper without any kind of nursing dissertation help.
    We keep things very simple at MyAssignmenthelp.com. All our services that offer nursing dissertation help online are easy to avail. And most importantly, they cater to the specific needs of your dissertation. Just let us know about your requirements, and we will deliver the much-needed assistance accordingly.
    Philosophy dissertation help

    ReplyDelete
  26. I(Elizbath) express that All the understudy needs to do is to connect with us, feed us the necessities of the undertaking related to any academic field and we will ensure that the assignment work is adequate. Purchaser reliability is our primary need and there is 100% affirmation that our understudies will score best grades in the assignments gave by us To extra information addresses visit our site SPSS Help

    ReplyDelete
  27. Looking for essay help online ?. Want essay assignment help? Let’s have a look at our endeavors!MyAssignmenthelp AU have a range of professional writers ready to provide essay assignment help or essay help to the students presenting top quality essays, keeping in mind the instruction provided by their professors.

    ReplyDelete

  28. Harvard referencing is a note citation system to cite the academic papers or any important documents. This referencing generator tool is also known as the documentary style note. To include the process of referencing and citations in the academic paper is very important to increase the readability of the paper and it will eventually help students in scoring good grades. This Harvard citation generator tool has been designed to create the most accurate formatting and referencing style for your academic paper, that too within a matter of minutes. So all your confusion over Harvard citation and referencing style will be resolved when you select our online Harvard reference generator tool from Allessaywriter.com.

    ReplyDelete
  29. A debt of gratitude is in order for sharing this blog. An incredible data you shared through this blog. Keep it up and good luck for your future sites and posts. spss help

    ReplyDelete
  30. We know it becomes frustrating when we got stuck with an academic paper that seems impossible to solve. Well, we have the perfect solution for you. Just avail our academic paper writing service in three simple steps and submit an impeccably drafted paper within the instructed deadline. No matter how complex or uncommon the problem is, we have the necessary resources to deal with it easily.

    Writing help is one of the oldest running paper writing services on the internet that has been consistent in helping students with their academic needs. In fact, we have introduced a number of custom paper writing service Singapore that can solve your specific needs with perfection. So, place an order today and see a positive change in your academic performance.

    ReplyDelete
  31. Assignment Help Sydney offered by skilled and experienced writers of Assignment Studio

    ReplyDelete
  32. My assignment help was already offering the services at the lowest price in the market.
    Myassignmenthelp shines like a bright star.
    I've received so much referral credits that now I can order an assignment service for me without digging into my pocket money. This is why I love Myassignmenthelp review.
    Must Read Free education to student.

    ReplyDelete
  33. Amazing knowledge and I like to share this kind of information with my friends and hope they like it they why I do dissertation writing services

    ReplyDelete
  34. Essay writers Australia service by Australian assignment help. Do you need the premium quality essay writing help, then look no more search. We provide instant assignment help in Australia. We are offering amazing writing services at low price.

    ReplyDelete
  35. A decent blog consistently concocts new and energizing data and keeping in mind that perusing I have feel that this blog is truly have every one of those quality that qualify a blog to be a one. assignment helps

    ReplyDelete
  36. I will be interested in more similar topics. i see you got really very useful topics , i will be always checking your blog thanks Buy Instagram Followers

    ReplyDelete
  37. I have read your excellent post. This is a great job. I have enjoyed reading your post first time. I want to say thanks for this post. Thank you... love & co review

    ReplyDelete
  38. I adore your websites way of raising the awareness on your readers. ent specialist singapore

    ReplyDelete
  39. Amazing knowledge and I like to share this kind of information with my friends and hope they like it they why I do ent specialist singapore

    ReplyDelete
  40. MyAssignmentHelp is the best assignment help website that is available for the students in Australia where they can avail my assignment help australia. It provides best assignment services not only to the students residing in Australia but also to the students living outside the country.

    ReplyDelete
  41. Peruse your blog entry and this is a pleasant blog entry. A debt of gratitude is in order for setting aside the effort to impart to us. have a pleasant day.I need to shear to All a major rebate offer with discount code. Helena Quinn

    ReplyDelete
  42. There are several assignment levels and techniques that professors ask you to complete. However, the lectures are not enough for that. You need external help to complete your assignment. So, you can easily search to do my assignment for me. It will do most of the assignment work.

    ReplyDelete
  43. Taking assignment orders and just randomly fulfilling the needs is not something that our expert writers do at My Assignment Help. Our My Assignment Help services are of top quality, for every assignment that we deliver, we make sure that we deliver best quality papers.

    ReplyDelete
  44. There are many thesis writing service providers available in market as this service is highly availed by many students.

    ReplyDelete
  45. At myassignmenthelp, we ensure that our customers receive original work every time they place order. Our expert writers are expected to produce customized assignment papers to reassure quality and content originality. Our expert writers are well aware of the rule concerns of the top universities in Australia, so they go the extra mile to reassure 100% plagiarism free content.

    ReplyDelete
  46. Admiring the time and effort you put into your blog and detailed information you offer!.. estee lauder night repair

    ReplyDelete
  47. I will be interested in more similar topics. i see you got really very useful topics , i will be always checking your blog thanks estee lauder advanced night repair

    ReplyDelete
  48. We are cabinet and granite experts specializing in kitchen and bathroom remodeling. Georgia Cabinet Company is proud to offer luxury cabinets and granite to all Georgia residents. Whether you’re looking for new cabinets/granite or a full remodel, our team will enhance the appearance of your home. Our goal is your satisfaction! Granite Atlanta, GA

    ReplyDelete
  49. We are cabinet and granite experts specializing in kitchen and bathroom remodeling. Georgia Cabinet Company is proud to offer luxury cabinets and granite to all Georgia residents. Whether you’re looking for new cabinets/granite or a full remodel, our team will enhance the appearance of your home. Our goal is your satisfaction! Kitchen Remodel Atlanta, GA

    ReplyDelete
  50. JP Scalpworx is a company that provides Scalp Micropigmentation. Scalp micropigmentation (SMP) is a non-surgical hair loss treatment that provides immediate and unrivaled results for men and women of all races and hair types. SMP is the most affordable long-term hair loss solution that provides undetectable, instant and maintenance-free results. We treat the following conditions: male-pattern hair loss, female-pattern hair loss, hair transplant enhancement, alopecia, scar concealment and repair SMP from other providers. Our clients are local to the Atlanta, GA area. Hair Transplant Atlanta, GA

    ReplyDelete
  51. JP Scalpworx is a company that provides Scalp Micropigmentation. Scalp micropigmentation (SMP) is a non-surgical hair loss treatment that provides immediate and unrivaled results for men and women of all races and hair types. SMP is the most affordable long-term hair loss solution that provides undetectable, instant and maintenance-free results. We treat the following conditions: male-pattern hair loss, female-pattern hair loss, hair transplant enhancement, alopecia, scar concealment and repair SMP from other providers. Our clients are local to the Atlanta, GA area. Hair Loss Atlanta, GA

    ReplyDelete
  52. Fundamental language is essential to shape an article or blog, these all thing, I can get in your article. I am bright about your association article, heaps of appreciative, I ought to urge you about the Australian task help to make the task rapidly.assignment helps

    ReplyDelete
  53. This website is remarkable information and facts it's really excellent memory foam mattress

    ReplyDelete
  54. Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. memory foam mattress

    ReplyDelete
  55. This is a wonderful article, Given so much info in it, These type of articles keeps the users interest in the website, and keep on sharing more ... good luck. situs idn poker

    ReplyDelete
  56. A good blog always comes-up with new and exciting information and while reading I have feel that this blog is really have all those quality that qualify a blog to be a one poker idn terbaik

    ReplyDelete
  57. I really enjoy reading and also appreciate your work. gila bola

    ReplyDelete
  58. I adore your websites way of raising the awareness on your readers. gila bola

    ReplyDelete
  59. I am looking for and I love to post a comment that "The content of your post is awesome" Great work! Sengkang grand residences price

    ReplyDelete
  60. This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information... Parc canberra ec

    ReplyDelete
  61. Always so interesting to visit your site.What a great info, thank you for sharing. this will help me so much in my learning Parc canberra price

    ReplyDelete

  62. Is this your first day in college and your professor assigned the first English essay writing service task? You are willing to impress your professor with a remarkable essay, but you do not possess remarkable essay writing skills. Even the natural writers struggle hard to write a perfect essay for the semester. You don’t have to be an amazing writer to crush your first essay. A handful of essay writing tips can do wonders.

    Essay writing is not a big deal for our experts who have been functional in the academic industry for over a decade. Our professional English essay writers are well-versed with proposal essays, narrative essays, exploratory essay topics, expository essays, etc. No matter how challenging your topic is, our cheap essay writing service team will certainly help you out.

    ReplyDelete
  63. Hi, I log on to your new stuff like every week. Your humoristic style is witty, keep it up read more

    ReplyDelete
  64. I really enjoy reading and also appreciate your work. read this

    ReplyDelete
  65. wow... what a great blog, this writter who wrote this article it's realy a great blogger, this article so inspiring me to be a better person buy tiktok likes

    ReplyDelete
  66. I really enjoy reading and also appreciate your work. buy followers on tiktok

    ReplyDelete
  67. Profesörünüzü dikkat çekici bir deneme ile etkilemeye hazırsınız, ancak dikkate değer deneme yazma becerilerine sahip değilsiniz. Doğal yazarlar bile dönem için mükemmel bir makale yazmak için zorlanırlar. İlk denemenizi ezmek için inanılmaz bir yazar olmanıza gerek yok. Bir avuç kompozisyon yazma ipucu harikalar yaratabilir.

    Betpas
    Betpas
    Betpas
    Vdcasino
    Vdcasino

    ReplyDelete
  68. What are the ten greatest and a wonderful digit major search engines scheduled for the planet? Aside from Google.com and Bing.com it additionally incorporates additional search engines that exist not notable but rather meet large many search inquiries each day. It capacity be an astonishment for some folks yet today Google does not have a nearby search motor happening the web! Actually, there are many search engines to facilitate require taking Google’s royal location, yet none of them is ready to confront any threat. In any case, there are search engines with the aim of advantage considering and list of all search engines are offered beneath. Top ranking list of search engines

    ReplyDelete
  69. What are the ten greatest and a wonderful digit major search engines scheduled for the planet? Aside from Google.com and Bing.com it additionally incorporates additional search engines that exist not notable but rather meet large many search inquiries each day. It capacity be an astonishment for some folks yet today Google does not have a nearby search motor happening the web! Actually, there are many search engines to facilitate require taking Google’s royal location, yet none of them is ready to confront any threat. In any case, there are search engines with the aim of advantage considering and list of all search engines are offered beneath. Top ranking list of search engines

    ReplyDelete
  70. I really appreciate this wonderful post that you have provided for us. I assure this would be beneficial for most of the people. Thanks for sharing the information keep updating, looking forward to more posts.

    High Quality Adult Images

    ReplyDelete
  71. Students from different parts of the world rely on our service, as we are providing secure payment gateways, confidentiality agreements and financial aid centers for communication. Marketing Dissertation Help

    ReplyDelete
  72. HP desktop/laptop, printer, scanner and other peripheral devices performed well at the workplace. There are thousands of customers who have query regarding HP devices. Contact HP Support Phone Number if you have any query regarding HP device.

    ReplyDelete
  73. Great Article it its really informative and innovative keep us posted with new updates. its was really valuable. thanks a lot. buy legal highs bath salts

    ReplyDelete
  74. I have read your excellent post. This is a great job. I have enjoyed reading your post first time. I want to say thanks for this post. Thank you... legal highs bath salts

    ReplyDelete
  75. best assignments strongly believes that all the students deserve to be successful, which is why their brilliant essay help experts have buckled up, to help students belonging to different study programs out of the stress, and into the success! From essays to case studies, this is the hub of ultimate assignment help!

    ReplyDelete